What’s up with physics?

Although I’m reasonably smart, I don’t have a high enough IQ to understand things like quantum mechanics.  At least I didn’t until I came across David Deutsch’s explanation; it’s all about fungibility. Being an economist, fungible is a concept that I do understand:

It is a rather counter-intuitive fact that if objects are merely identical (in the sense of being exact copies), and obey deterministic laws that make no distinction between them, then they can never become different; but fungible objects, which on the face of it are even more alike, can.  This is the first of those weird properties of fungibility that Leibniz never thought of, and which I consider to be at the heart of the phenomena of quantum physics.

Here is another.  Suppose that your bank account contains a hundred dollars and you have instructed your bank to transfer one dollar from this account to the tax authority on a specified date in the future.  So the bank’s computer now contains a deterministic rule to that effect.  Suppose that you have done this because the dollar already belongs to the tax authority.  .  .  .  Since the dollars in the account are fungible, there is no such thing as which one belongs to the tax authority and which one belongs to you.  So we now have a situation in which a collection of objects, though fungible, do not all have the same owner!  Everyday language struggles to describe this situation: each dollar in the account shares literally all its attributes with the others, yet it is not the case that all of them have the same owner.

.   .   .

The term ‘uncertainty principle’ is misleading.  Let me stress that it has nothing to do with uncertainty or any other distressing psychological sensations that the pioneers of quantum physics might have felt.  When an electron has more than one speed or more than one position, that has nothing to do with anyone being uncertain what the speed is, any more than anyone is ‘uncertain’ which dollar in their bank account belongs to the tax authority.  The diversity of attributes in both cases is a physical fact, independent of what anyone knows or feels.

Nor by the way, is the uncertainty principle a ‘principle’, for that suggests an independent postulate that could logically be dropped or replaced to obtain a different theory.  In fact one could no more drop it from quantum theory than one could omit eclipses from astronomy. (From the multiverse chapter in “The Beginning of Infinity.)

This blew my mind, and so I decided to check with Eliezer Yudkowsky, who most definitely does have a high enough IQ to understand QM:

So let me state then, very clearly, on behalf of any and all physicists out there who dare not say it themselves:  Many-worlds wins outright given our current state of evidence.  There is no more reason to postulate a single Earth, than there is to postulate that two colliding top quarks would decay in a way that violates conservation of energy.  It takes more than an unknown fundamental law; it takes magic.

The debate should already be over.  It should have been over fifty years ago.  The state of evidence is too lopsided to justify further argument.  There is no balance in this issue.  There is no rational controversy to teach.  The laws of probability theory are laws, not suggestions; there is no flexibility in the best guess given this evidence.  Our children will look back at the fact that we were STILL ARGUING about this in the early 21st-century, and correctly deduce that we were nuts.

We have embarrassed our Earth long enough by failing to see the obvious.  So for the honor of my Earth, I write as if the existence of many-worlds were an established fact, because it is.  The only question now is how long it will take for the people of this world to update.

Ha!  So most of those arrogant physical scientists who make fun of how “unscientific” we social scientists are, don’t even follow the scientific method in the supposed “queen of the sciences”—physics.  Modern physicists are no better than the Pope who insisted that Galileo could use his heliocentric theory, but only if he admitted it was merely for prediction, not as a description of “reality.”   “Hey Galileo; shut up and calculate.”  Pathetic.

And it’s not just the physicists; how often have you heard some younger New Keynesian, or New Monetarist, or  New Classical-type prattle on about how “real economists” use mathematical models (preferably DSGE), and that we followers of the old Chicago School (i.e. Milton Friedman) weren’t “serious scientists.”  I can’t wait to tell them what “serious science” says about reality.  Here’s Deutsch:

All fiction that does not violate the laws of physics is fact.

So there are universes where Market Monetarism is true.  Take that you science fascists!

(Unfortunately that also means there are universes where MMT is true.  However I’d wager they are of googleplex orders of magnitude smaller “measure.”)

It’s also good to find out that the multiverse is deterministic.  When I was young I argued with the first guy who told me that QM implied a random universe.  It made no sense to me.  OK, our universe is random, but the multiverse isn’t.  That’s what I meant.

Now let’s try to relate this stuff to NGDP.  Here’s my analogy.  If there is a negative NGDP shock then employment falls in the short run.  But if the NGDP shock is quickly reversed then our universe joins up again with the universe that did not have the negative NGDP shock.  (Imagine the negative shock only occurs in one of the two universes, because Ben Bernanke’s mind is put into a Schrodinger cat-type experiment, where a particle’s behavior determines whether his mind will lose all memory of the need for Rooseveltian Resolve.)

Unfortunately, the NGDP shock may become “entangled” with the other parts of the economy, which could lead to “decoherence.”  I can think of two types of entanglement:

1.  The negative NGDP shock leads to lower nominal wages before NGDP is restored to the old path.  In that case restoring NGDP pushes employment above the natural rate.

2.  More likely the negative NGDP shock leads to bad supply-side policies, such as extended UI benefits.  When NGDP returns to normal, employment remains below the natural rate.

Any other applications of QM to macro?

PS.  If our students can’t understand that money is fungible, how the hell are they going to understand that they themselves are fungible!

PPS.  If you think I’m being modest about not having a high IQ, then consider that even after reading Deutsch and Yudkowsky, I still find it hard to believe there is enough room for all these universes.

PPPS.  My rant against economists’ obsession with models reminds me of this recent Nick Rowe post:

If the real world really were as simple as my simple model, then price controls really would be a good thing, in both the short and long run. But the real world is much more complicated than my ability to model it, so I think that price controls will be a bad thing, at least eventually. But I can’t model it, because it’s too complicated for me to model.

I think that it is thoughts like this that drive Austrian economists to distraction. I sympathise. I think they are right. The, um, medium of modelling biases the message.

Love that last sentence.

PPPPS.  Don’t believe anything is possible?  Read this.


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80 Responses to “What’s up with physics?”

  1. Gravatar of marcus nunes marcus nunes
    9. February 2013 at 06:39

    Yes, GWB as painter clinched it!

  2. Gravatar of Suvy Suvy
    9. February 2013 at 06:46

    “When an electron has more than one speed or more than one position, that has nothing to do with anyone being uncertain what the speed is, any more than anyone is ‘uncertain’ which dollar in their bank account belongs to the tax authority.”

    This kind of uncertainty is very different between the kind of uncertainty that occurs in economics. Even with Heisenberg’s Uncertainty Principle, the degree of uncertainty is knowable because the amount you can know about the momentum and position of a particle is normally distributed. However, in economics there is absolutely no way to do this because there is no such thing as statistically independent samples. For example, if I take 10 years of data on interest rates, the first year of interest rates plays a part in what interest rates will be the next year.

    “The laws of probability theory are laws, not suggestions; there is no flexibility in the best guess given this evidence”

    The laws of probability are laws; however, the laws of probability cannot be used in economics for the very reason that I stated earlier. There is no such thing as statistically independent sampling in economics; so almost all sorts of statistical tools cannot really be used to determine future events.

    In physics, you can isolate variables in labs. In economics, you’re dealing with behavior of humans that is dependent on psychology, luck, and the fact that one person’s behavior affects 20 other things which again affect his behavior. The methods that are used in physics cannot be used in economics.

    Mandelbrot primarily used power law probability distributions rather than the normal distributions that are usually seen. I think that’s the right approach because in many areas of economics, you see a scaling effect(see Pareto principle). The problem with power law distributions is that due to the shape of the distributions and the “fat tails”, you can’t get very much out of trying to sample from the real world. Almost all of the statistical tools and econometrics tools fail; this is the first thing you learn in any sort of graduate level time series analysis class or graduate level probability/statistical theory class or anything similar.

  3. Gravatar of marris marris
    9. February 2013 at 07:37

    Check out this post on the many-worlds interpretation (MWI) by Scott Aaronson. He’s great on this stuff.

    http://www.scottaaronson.com/blog/?p=1103

    [He also enjoys reading David Deutsch]

  4. Gravatar of Neal Neal
    9. February 2013 at 07:58

    The EM hypothesis is a lot like Schrodinger’s cat. Given a range of possible outcomes to an experiemnt, the market’s state is the expected outcome. When the experiment actually occurs, the market “collapses” its “waveform” to the actual outcome of the experiment.

  5. Gravatar of Neal Neal
    9. February 2013 at 07:59

    (When I say the market’s state is the expected outcome, I mean that the market is a superimposition of all possible outcomes weighted by their probability.)

  6. Gravatar of Jon Jon
    9. February 2013 at 08:07

    http://motls.blogspot.com/2012/11/many-worlds-vs-positivism-and-symmetries.html

  7. Gravatar of Visitor Visitor
    9. February 2013 at 08:18

    Don’t believe that MWI is indisputably established. It’s nothing of the sort and an extended, emphatic rant claiming so without a single reference to an experiment that demonstrates the claim shouldn’t sway you.

  8. Gravatar of Rich C Rich C
    9. February 2013 at 08:55

    MWI apostles use equations to conjure the universe, rather than the universe to conjure equations.

  9. Gravatar of Jason Jason
    9. February 2013 at 09:37

    The key word is “interpretation” … the many worlds interpretation of quantum mechanics makes no additional predictions vs quantum mechanics as yet that are testable. Other “interpretations” are wrong — if you used them as intuition you’d get incorrect answers in calculations or they have been experimentally invalidated. Other interpretations (e.g. Transactional from John Cramer who I know) are also correct in the sense the many worlds interpretation is correct.

    QM interpretations are closely related to interpretations of probability, just with more dynamics.
    http://en.wikipedia.org/wiki/Probability_interpretations

    There is no a priori reason that reality should be explainable in some sort of “common sense” human language (what it means to have an interpretation). However! Galileo was actually describing a common sense reality — his (and Newton’s) laws are loosely speaking valid from atoms to planets. Quantum mechanics is necessary from atoms on down and general relativity is necessary at the scale of stars and above. There should be an interpretation of Newton’s laws; they exist at our scale. There is no reason there should be an interpretation of quantum mechanics. The funny thing is that there really isn’t an “interpretation” of Newton’s laws. We don’t seem to need some analogy with frames of film or collapsing functions to explain why the solution to the deterministic gravitational equations for the three body problem is chaotic. I’m not sure why that is. Probably because chaotic motions are part of our normal life in the form of flocks of birds and the branches of trees.

    Of course, even quantum mechanics may be wrong at the Planck scale … therefore the many worlds interpretation of it may be incorrect as well.

    But contra Eliezer (and related to Scott’s point about there being enough room for many worlds) there effectively is a single Earth, even if the many worlds interpretation is correct. The physical laws that govern it do not depend (strongly) on QM. In my own mind, I think of it as a kind of convergent compression as you zoom out on a scene … the information required to store the differences between the many universe “frames of film” becomes smaller relative to the total amount of information as you zoom out from where quantum effects are important. It’s like a DVD … for an action sequence, a lot more data is stored since frames are very different (say, zoomed in on atoms). For a establishing shot, there are usually limited differences between frames (say, zoomed out to show the Earth). This is an interpretation and it is likely wrong, otherwise — where is my Nobel prize? Kidding aside, the main point is that saying quantum mechanics describes reality is different than saying quantum mechanics describes reality in this way (a particular interpretation).

    [For the physicists in the room, I am thinking about the information encoded on the holographic screen at the boundary, and as R -> infinity, the number of bits ~ R^2, while the number of different many worlds "frames" is related to the number of particles N in a causally connected patch ... for some R, R^2 is even bigger than N! or whatever measure you'd like for the number of possible universes. The many worlds interpretation has never show in a satisfactory way where the information for all these universes is stored consistent with what we know from black hole information theory i.e. Scott's common sense point about there being enough room ... there's even less if the information is only encoded on the boundary!]

  10. Gravatar of mbk mbk
    9. February 2013 at 09:44

    Neal: beautiful.

  11. Gravatar of Kevin Dick Kevin Dick
    9. February 2013 at 10:29

    I think there is probably some correlation between people who accept MWI and MM.

    When I first read Eliezer’s explanation of MWI years ago, it felt like my entire brain clicked into place. I went back and read several books on QM and all of a sudden they made intuitive sense rather than just mathematical sense.

    Same with MM. I had written off the macro side of economics as a collection of just-so stories (aside: John Taylor was my intro lecturer). Then I read your blog for the first time, and got that same brain-clicking feeling.

  12. Gravatar of ssumner ssumner
    9. February 2013 at 10:53

    Marcus, The paintings are actually pretty good. Bush is a better painter than Hitler was. (Picking 2 politicians at random.)

    Suvy, I don’t see the relevance . . .

    Marris and Jon, Thanks for the links.

    Neal, Great analogy! Better than mine.

    Visitor. I’m afraid that’s not how science works, or is supposed to work. Obviously the MWI might be disproved at some point, just as Newtonian physics was superseded by relativity, particularly the interpretation of gravity. But nonetheless back in 1800 no physicist had a good reason for rejecting Newtonian physics, and saying that it might be superseded at some point is not a good reason. All theories are provisional. The question is whether the MWI is the normal straightforward intepretation of QM. Maybe not, but some pretty smart people seem convinced that it “obviously” is the straightforward interpretation, and other interpretations are convoluted and lack evidence. Obviously I’m in no position to judge, but Deutsch and Yudkowsky are awfully smart in areas where I am qualified to judge, so I take their critique seriously. (Maybe Eliezer will comment here.)

    I found the “rant” amusing, sorry you felt differently. I do know that it wasn’t a proof.

    Rich, I can’t see how the MWI theory isn’t “normal science.”

    Jason, Thanks for that info. Obviously I’m not qualified to comment. I hope it was obvious to everyone that I was just having some fun. I.e. half-joking and half-serious. The part about me pretending to have an intelligent opinion on QM was the half-joking part.

  13. Gravatar of ssumner ssumner
    9. February 2013 at 10:56

    Kevin, I’m honored.

  14. Gravatar of Suvy Suvy
    9. February 2013 at 10:58

    Prof Sumner,

    My comment was just to show the difference between the methodologies for something like physics vs economics. Economics simply cannot be scientific in the same way physics can due to the nature of the field. It was kind of unrelated.

  15. Gravatar of Patrick R. Sullivan Patrick R. Sullivan
    9. February 2013 at 11:13

    ‘The, um, medium of modelling biases the message.’

    The medium of modelling massages the message? Messes up?

  16. Gravatar of Don Geddis Don Geddis
    9. February 2013 at 11:37

    I had a similar experience to Kevin Dick. I immediately thought of the analogy, that Deutsch and Eliezer are to QM, what Sumner is to macro. Besides just coming up with the right answers, in both cases they are opposed by some very smart, well-educated, credentialed professionals in the field who disagree with those answers. So it’s confusing for outside laypeople. Moreover, Deutsch / Eliezer / Sumner didn’t really come up with the key insights themselves. From their perspective, the puzzle is that the field already knew the right answer; the question is, why did so many senior people ignore the obvious answer that was right in front of them?

    I think the lesson is: just because you’re really, really smart, and understand something that is very complex, doesn’t make you immune to all the usual irrational cognitive biases.

  17. Gravatar of Gene Callahan Gene Callahan
    9. February 2013 at 11:43

    ” Maybe not, but some pretty smart people seem convinced that it “obviously” is the straightforward interpretation…”

    Scott, MWI is a desperate attempt to save materialism from the massive counter-evidence QM offers. In a few hundred years people will be laughing about how anyone ever took this nonsense seriously.

    And note that MWI isn’t even a scientific theory: it is a metaphysical suggestion. We could never reach or find or see these “multiple worlds,” and so there is no way on principle this theory could ever be falsified.

  18. Gravatar of Eliezer Yudkowsky Eliezer Yudkowsky
    9. February 2013 at 12:01

    Oh dear God did you just step into a nest of hornets. I never talk about quantum mechanics unless I *have to*.

    Some quick comments:

    1) The paragraph you quote from me, is from the concluding sequence of a long sequence of posts trying to explain QM. There’s several entries into this sequence, but for readers here I would recommend:

    http://lesswrong.com/lw/r6/an_intuitive_explanation_of_quantum_mechanics/

    The quoted paragraph is instead from content indexed by:

    http://lesswrong.com/lw/r8/and_the_winner_is_manyworlds/

    Comments on the OP:

    * Some physicists are in denial about MWI. It’s possible – polls vary – that an actual majority of theoretical physicists believe in many-worlds at this point. So criticizing “physicists” seems a bit unfair.

    * It also takes a lot of work to see MWI as “obvious”, and it’s safe to assume that many audiences will have no idea what you’re talking about when you say that. I.e., they’ll think you’re crazy. If you’re willing to dare that, go ahead…

    * Deutsch’s “All fiction that does not violate the laws of physics is fact” can be viewed as a consequence of the universe being spatially large, never mind QM – if the universe is indefinitely large, then if you travel far enough away, any physical possibility will be realized (albeit perhaps with very low frequency). IIRC, the usual calculation is that an exact copy of our local Hubble volume should exist no more than 10^(10^119) meters away from this one. There’s only so many ways you can pack particles into a few billion lightyears. Quantum mechanics doesn’t add any plenitude that isn’t already present in a spatially unbounded universe.

    * However, it doesn’t seem to me certain that there are distant Hubble volumes (or equivalently, other quantum branches) where market monetarism is true. I take MM to be the conjoined statement that (1) people behave in certain microeconomic ways, and (2) if people behave in those ways then NGDP instability does more RGDP damage than inflation instability, and hence, a central bank which tries to stabilize NGDP will promote more RGDP growth than one which tries to stabilize inflation. If (2) follows logically from (1) but (1) is empirically false in our world, and yet (1) is realizable elsewhere, then market monetarism is true on some distant alien planet where entities behave in a different microeconomic way (the way Scott Sumner thought people behaved) and hence market monetarism is true in their world. But if (2) is in fact logically incompatible with (1) then market monetarism contains a logical falsity and need not be true anywhere.

    * If MMT doesn’t contain logical falsities then it is realized in worlds much more probable than “googolplex orders of magnitude less” because that’s 10^-10^10^100 which is, like, way more improbability than you need to have all the particles in the galaxy spontaneously rearrange into a giant flying spaghetti monster. (Robin Hanson makes a good case that worlds this improbable may fail to exist because they would be dominated by tiny bits of stray amplitude from larger worlds; Google “mangled worlds”.)

    *) The remark about NGDP-shock universes merging back into the mainstream after a policy correction is clear to me as a metaphor. Quantumly speaking that can’t *actually* happen unless you erase all memories of the NGDP shock and end up in *exactly* the same universe. This in turn is difficult because of, well, “technical reasons” (Liouville’s Theorem). But the metaphor is clear to me regardless.

  19. Gravatar of Gene Callahan Gene Callahan
    9. February 2013 at 12:56

    Here is a physicist who sees this for what it is: MWI is “pseudo-scientific ideology.”

  20. Gravatar of Gene Callahan Gene Callahan
    9. February 2013 at 13:10

    Scott, here is cosmologist Bernard Carr explaining exactly why people like the multiverse idea: “If there is only one universe, you might have to have a fine-tuner. If you don’t want God, you’d better have a multiverse.”

    Desperation.

  21. Gravatar of Neal Neal
    9. February 2013 at 13:42

    Another analogy: the Law of One Price basically says that prices obey a heat-type equation.

  22. Gravatar of W. Peden W. Peden
    9. February 2013 at 15:48

    Well, the main thing I’VE learned in this thread is that there are debates in physics that as just as impolite and full of bluster as many debates in economics, which is both relieving and disappointing.

  23. Gravatar of Don Geddis Don Geddis
    9. February 2013 at 16:54

    @W. Peden: Exactly. The way high-status people in an organization interact, is a matter of human psychology and sociology. Thomas Kuhn’s “paradigm shift” often happens, not because the senior scientists are convinced to change their minds, but instead because the old generation eventually dies off, and the new younger generation is more open-minded about the benefits of the new paradigm.

  24. Gravatar of mbk mbk
    9. February 2013 at 19:27

    To expand on W. Peden, it is not clear to me to what extent either physics or economics have progressed from the ages where we’d all have been discussing angels on pinheads.

  25. Gravatar of Jon Jon
    9. February 2013 at 21:22

    Scott writes: “Marris and Jon, Thanks for the links.” and also in the OP “So most of those arrogant physical scientists who make fun of how “unscientific” we social scientists are, don’t even follow the scientific method in the supposed “queen of the sciences”—physics.”

    Sorry I didn’t have time to explain earlier, If you look into Motl’s history/background you’ll find quite the irony in connection with this post. I provided the link because he rejects the multi-worlds interpretation… but he was also basically ejected from his asst professorship at Harvard for very publicly berating some well known tenured physics for promoting interpretations of physics that he thought demonstrated their failure to master QM.

    Some people really had their feathers ruffled by them and you can find rants which disparagingly cite comments from him such as:

    “I think it is an absolutely paramount requirement for science to eliminate answers that can be shown to be wrong and, at the sociological level, to eliminate the people who have shown that they are only able to produce wrong answers. — Lubos Motl

    Yeah, he is not a polite guy, but it’s kind of comical that among the quotes circulated to disparage him, we get one where he says we should work to filter out bad ideas. The horror!

  26. Gravatar of David Kagan David Kagan
    9. February 2013 at 21:25

    Hi Scott,

    I’m a theoretical physicist who has been enjoying your blog now for about two years, and finally you’ve written about something I feel qualified to comment on!

    I have to *strongly* disagree with the rather triumphalist attitude about Many-Worlds that is presented here.

    Many-Worlds is one of several interpretations of quantum mechanics, most of which have a reasonable number of firm adherents. There is *no* consensus about which interpretation is all-out correct (I recommend asking around some of the local physics departments to see what answers you get).

    The only consensus about quantum mechanics is in how to apply it to the vast majority of problems that physicists deal with: predicting the statistical behaviors of particles when they are measured in various ways. There is a basic recipe for this and we all know how to follow it. Physicists who don’t ask too much about what it all means are part of what is called (I think mostly jokingly) the “shut up and calculate” school.

    Many-Worlds has some very nice features: it highlights the deterministic aspects of quantum mechanics quite nicely. It appears to have a good answer to the problem of collapsing the wavefunction (it only looks like collapse to us, but across the “branches” of the many worlds, there is no collapse).

    But some of its nicest features lead to some of its weakest points as an interpretation. The most critical problems have to do with the nature of probability. In quantum mechanics, probabilities are calculated according to a certain rule (the Born rule). One of the features of many-worlds that was *supposed* to be appealing was that this rule was meant to be derivable. It is *not*—not if one insists that the only postulates one keeps are the ones that involve neither collapse nor the Born rule.

    The other issue is that, even if you grant that the Born rule is the right way to calculate probabilities, you still have to ask what those probabilities even mean? If every outcome happens, then the probability that your future self will see some experimental outcome equals one. You might argue that the probability refers to which one of those future selves you yourself have the experience of, but the answer is that you are going to be all of them! These problems are closely related to something called self-locating probability problems, and they are very thorny.

    I’m not saying that there aren’t clever—very clever—answers to some of these issues. But from my perspective, those answers lard on a lot more structure than what originally got you to consider Many-Worlds in the first place. I think Eliezer would agree (it looks like he does in a comment above) that understanding Many-Worlds is highly non-trivial. It is by no means an interpretation that jumps out at everyone as solving all the problems of thinking about quantum mechanics.

    I like Many-Worlds—I think that it can be useful to use this interpretation to frame certain issues in quantum theory. But there are other approaches that I find at least as compelling, such as thinking of quantum mechanics as a generalization of standard probability theory.

    Incidentally, regarding the whole Queen of the Sciences thing—I hate that. Physics can get very far in making very precise statements and predictions because it deals with very simple systems, or it focuses on the simple aspects of certain systems. It’s the simplicity of the electron—all of them are absolutely identical!!—that allows us to model them in such a powerful fashion.

    All that being said, our inability to find a consensus position on the correct interpretation of quantum mechanics is not something that should be strongly held against us. We are studying a theory whose key effects become noticeable at the scale of a modest number of atoms (if one is being very careful). We should always be open to the possibility that the nature of the quantum world is not entirely compatible with what we consider to be satisfying explanations. Physicists should be judged by the consistency and applicability (both in the sense of material and intellectual uses) of our theories, and by that standard I think we do a pretty good job.

  27. Gravatar of David Kagan David Kagan
    9. February 2013 at 21:27

    P.S. Reading over this, I can’t help but feel that it would be a good example of arguing at the top of our lungs because the stakes are just so small!

    P.P.S. But that said, we are talking about understanding the fundamental nature of reality here!

  28. Gravatar of ssumner ssumner
    10. February 2013 at 07:42

    Don, Very interesting point.

    Gene, So what’s the alternative model?

    BTW, I’m not saying the MWI is true, that’s not the issue. Newton’s theory of gravity was not true, but scientists in 1800 had no good reason not to believe it.

    Eliezer, You said;

    “way more improbability than you need to have all the particles in the galaxy spontaneously rearrange into a giant flying spaghetti monster.”

    That’s sort of what I had in mind for MMT. Seriously, you are right of course.

    Neal, I’m afraid I haven’t studied heat equations.

    Jon, Interesting story.

    David, You said;

    “If every outcome happens, then the probability that your future self will see some experimental outcome equals one. You might argue that the probability refers to which one of those future selves you yourself have the experience of, but the answer is that you are going to be all of them! These problems are closely related to something called self-locating probability problems, and they are very thorny.”

    I’m having trouble seeing the problem here. It seems to me it is merely a question of semantics. If “you” means “all futures yous” then there is a 100% chance of at least one of “you” seeing a certain event. But if it refers to just one of the many future yous, then it would be a smaller probability. It’s clear to me what’s being described here; it seems to me we are getting tripped up over terminology. But then maybe I completely misunderstand.

    Good comment overall, of course keep in mind I was half joking here.

  29. Gravatar of Mike Rulle Mike Rulle
    10. February 2013 at 08:04

    I am glad David Kagan wrote what he did, as he is a real physicist. I am merely a dedicated follower of fashion who reads books written by physicists for the general public. As someone who is fascinated with probability theory in general, it never was strange to me to think QM as a generalization of standard probability theory. Many physicists are fascinated with the difficulty of squeezing QM into a new common sense heuristic—or changing the common sense heuristic into an almost mystical phenomenon.

    I forget which of the early to mid 20th century physicists was the creator of the “shut and calculate” school, but that was always sufficient for me. It predicts correctly—that is the point.

    My understanding of MW theory is that it gets the same answers as shut up and caculate, but no more. Brian Greene, a writer for the masses, believes someday an experiment can be constructed to test these new theories. I think it likely MW is a wonderful (currently untestable) internally consistent construct. But I also believe math is malleable. Converting it into a MW “new common sense” however is quite another thing all together.

    I am well beyond my knowledge point here. But physicists are arguing about realms unrelated to what QM is capable of doing in our hear and now. My understanding is in our hear and now they get the same answers. And they are quite good at it.

    Unfortunately, in Economics, we are not even close. We have a hard time getting any answers.

    But I still love economics as it is central to the mysteries of our human existence.

  30. Gravatar of Neal Neal
    10. February 2013 at 08:39

    Scott – I just mean that a price spreads out the way heat spreads out in an object. For example, http://www.youtube.com/watch?v=_bVhU9Qv5JY

    On the discussion of probabilities, let’s not forget that the methods physicists use to compute probabilities of interactions don’t currently have a rigorous mathematical basis. (Feynman integrals aren’t integrals, renormalization makes no mathematical sense, etc.)

    As far as I’m concerned, the only thing QFT has going for it is that somehow, this method of pushing symbols around *works* (as Feynman put it, the equivalent of measuring the distance between New York and LA to the width of a single human hair).

  31. Gravatar of Don Geddis Don Geddis
    10. February 2013 at 09:12

    @David Kagan: What’s ironic, is the the bulk of what you say is not actually in opposition to what Eliezer says (here, and in his Sequences). And yet you “strongly disagree”, despite agreement on essentially all the details.

    You are right that there is no consensus for QM interpretation in the field of physics. Eliezer’s point is that this is because physicists do not automatically come with skills in philosophy or rationality. But it is not because physicists know something that the rest of us don’t understand.

    You say that MWI was “supposed” to derive the Born rule; this actually isn’t a benefit claimed by MWI adherents. The Born rule is a puzzle, but it’s a puzzle for all interpretations, so it’s not relevant to distinguishing between them.

    You’re right that MWI is not obvious at first glance. The point is, that the people who have studied it, have no excuse for not (provisionally) accepting it.

    Sumner has the correct conclusion: MWI is not “true”, but it’s just like Newton’s gravity in 1800. People who refuse it, given current evidence, are not being rational.

  32. Gravatar of Eliezer Yudkowsky Eliezer Yudkowsky
    10. February 2013 at 09:43

    David, since you’re already familiar with the issues, I think I’d point you at:

    http://lesswrong.com/lw/q7/if_manyworlds_had_come_first/

    though the original page Scott linked is also an okay summary.

  33. Gravatar of W. Peden W. Peden
    10. February 2013 at 09:45

    Don Geddis,

    It’s best not to set me off on Kuhn. I’ll just say that I agree with what YOU’RE saying!

    mbk,

    I don’t doubt at all that there has been progress in both disciplines, but I think that human beings are very imperfect and the universe is very complex, so scientific progress is slow, erratic, filled with cul-de-sacs, and has been largely a recent phenomenon when measured against human history as a whole. This moderately pessimistic view has the optimistic edge that I don’t have to think that anyone is particularly venal or moronic to disagree with me!

  34. Gravatar of J J
    10. February 2013 at 09:52

    Neal – regarding your analogy between the EMH and QM…

    You are mistakenly thinking that QM is just about a lack of information. A stock price is the expected value of possible outcomes, and once we have more information, the price adjusts accordingly. Yet, theoretically, there always was a correct price. The EMH can be true just because all humans are equally not smart enough to perfectly estimate the discounted sum of future dividends.

    On the other hand, QM is different from standard probability theory because, even theoretically, there is no definite position of an electron. Moreover, you can determine if an electron is spin up or spin down along one axis, but then once you determine if it is spin up or spin down along a perpendicular axis, the spin along the initial axis will revert to a superposition between spin up and spin down. The point is that probabilities in QM don’t reflect a lack of information, but rather a real superposition of states.

    More relevantly, I don’t think it is fair to compare disagreement over interpretations of QM (which is mind-bogglingly bizarre) to disagreement over simple things like whether money is tight in Japan or not. Especially because the interpretation of QM is not necessarily all that important, and physicists still agree on the predictions of QM and how to use it. I wish the same could be said of economists.

  35. Gravatar of David Kagan David Kagan
    10. February 2013 at 10:27

    Scott: I know you’re partially joking! I really enjoyed the post.

    You raise a point that I used to agree with—namely that the whole issue of who “you” is—and when!—is a semantic exercise. I still agree it’s semantic, but we’re talking about drilling down into what things actually mean, so understanding your semantic commitments is important. You have to at least formalize the intuitive response you had to the problem. The way I’ve seen this done is to say that the probability is the one that the future you would assign if he asked “which of the worlds have I ended up in” *after* the experiment is performed, but presumably before he looks at the result.

    On top of this issue however is the problem that the most naive approach to assigning such a probability does not reproduce the Born rule of quantum theory. If you set up a system that can stay whole or decay the naive thing to do is to say that since there are two distinct worlds, the probability should be 1/2 that you find yourself in either one. However, in quantum theory, you can set up states like this where the probability of decay is say, 10% and no-decay is 90%. The branching structure of the wavefunction (as looked at from a many-worlds perspective) tells you nothing about which probability measure is the right one (and in some ways many-worlds encourages a misleading view that each branch should be as good as any other).

    Don’t even get me started on the preferred-basis problem! Again, there are answers, but they won’t satisfy everyone—nor should they, necessarily.

    Scott, you’ve really opened up a can of worms here. And you thought that arguing for NGDPLT was asking for trouble!

    Don Geddis: you say that getting this probability measure is not something many worlds adherents believe. That may be true now (though I don’t think it is—ask Deutsch or Wallace!). But even if true now, this represents a pretty big retreat from some of the earlier claims by proponents of this interpretation.

    And while I entirely agree that physicists are not trained in “rationality”, there are some who are quite clearly very good at it. Look up Matt Leifer or Rob Spekkens—these guys are coming out of the quantum information theory side of things, they definitely do not adhere to many worlds, but are incredibly thoughtful about the various interpretations of quantum mechanics. I’m hesitant to cite philosophers of physics here, but since you want to talk about people with skills in philosophy and rationality, I’d point you to David Albert. I strongly disagree (there I go again!) with him too, but he’s probably one of the most prominent philosophers of science out there. He definitely does not buy many worlds.

    And it shouldn’t be too surprising that Eliezer and I agree on the vast majority of things we say about quantum mechanics. The math is very precise, we both now what it means in a technical sense—we’re definitely going to overlap in a big way. What I was strongly disagreeing with was the notion that there even should be a consensus about the interpretation of quantum mechanics in the physics community at this point. Again, many worlds has many good things going for it, but it is not the leader among interpretations in terms of evidence. Any no-collapse interpretation of the wavefunction that is careful not to contradict what is known about quantum theory and its experimental validity is a valid interpretation. Bohmian mechanics can be formulated in a manner that is totally consistent with everything we know. Perhaps it gets kludgey, but that’s a matter of taste. The Bohmians think many worlds is kludgey too.

    (I’m a fan of the terminology “Bohmians” and “Everettistas”. It sounds like an endless battle between various tribes of hipsters living in Brooklyn).

    Then there are interpretations where the wavefunction is treated epistemically. It isn’t something that exists out there in the world. Rather, it is a construction for assigning rational probabilities, much like the Bayesian view of standard probability theory (personally, I’d rather not focus on the wavefunction itself here, but the more general concept of density matrix…and yet, this is getting way too long as it is). In these interpretations, collapse is completely natural, since it is a form of updating an agent’s beliefs or knowledge about a system. Collapse is as mysterious as what happens when you update your probability distribution given new information using Bayes’ theorem.

    I can’t get too far into the thicket of why many worlds has no particular claim to being the best of all the interpretations out there. There’s just too much to discuss! But I urge you to check out the work of people like Leifer and Spekkens. As I said, many worlds is a useful tool to have in the kit, but so are other ways of looking at quantum theory.

  36. Gravatar of phil_20686 phil_20686
    10. February 2013 at 10:36

    I will push back against the MWI. I spent some time as a cosmologist, and cosmology presents some fairly unique problems for quantum mechanics.

    Firstly, I want to push back on the concept of “interpretation”. At the end of the day, we have theoretical constructions for the purpose of replicating observations. I can “interpret” Quantum field theory as long strings of harmonic oscillators, that clearly isn’t “real” but still makes a very useful viewpoint for introducing the mental framework of QFT, and at the end, when you understand it, you discard the “interpretation”, and have a theory which stands on its own. When you ask a physicist if MWI is correct, and they say yes, they might mean one of three things:

    (1) MWI has no conflict with any empirical result. Many other `interpretations’ are equally correct.
    (2) MWI adds some unique features that will lead to falsifiable predictions that I expect to one day see confirmed, which will invalidate all (most) other interpretations. The fact that the mathematical framework of MWI works better than other frameworks does not imply that these other worlds have a real physical existence.
    (3) The other worlds exist in some objective physical sense.

    My experience was that quite a lot of physicists believe (1). Some believe (2), and almost none believe (3) which seems to have been named “many worlds extremism”.

    As far as scientific objections go, there are plenty. Firstly, its unclear what constitutes a branching, de-coherence is more of a spectrum than a fixed point, its quite hare to believe that there is every really “complete de coherence”, which is problematic itself, as most of the interference arguments suppose that you get interference from each of the possible branches, but you can also get interference from old universes, and its possible for this to ruin the predictions. Of course, this is also the basis for some potentially falsifiable communication strategies.

    Further questions are raised by what happens when universes diverge and then become the same again, do you end up with two identical copies? Set ups like that used to verify bell’s inequality seem to end up with two copies of identical universes, which are only different on account of their past history, which is no longer relevant for future measurements. (Imagine measureing the spin of an electron three times, originally on some axis, then at 45 degrees to that axis, then on the original axis, you get eight branches based on all possible histories, but that gives you only two final results) so do I end up with two universes or 8 universes describing two possibilities.

    It seems inevitable that you end up with infinite copies of identical universes, as well as infinite different universes.

    Anyway, currently, as the physics stands, statement one is obviously true, just not very helpful. Statement two might or might not become empirically justified, and statement three seems impossible to differentiate even in theory from one universe with a sum over past histories, without even caring if they are “real” or not.

    Then there are the black hole+unitarity problems. What happens to the branches if a black hole starts devouring parts of the wave function so as to render the theory non-unitary. Its clearly possible to have branches that are devoured in their entirety by black holes before they can really propagate.

    So lots of problems, no imminient hope of falsification, and its not clear even if it was falsified that we would treat theise other worlds as anything other than a useful construction.

  37. Gravatar of David Kagan David Kagan
    10. February 2013 at 10:58

    phil_20686: I think you and I have raised some similar points.

    One thing though—information loss due to black holes is a radical position to take, especially since there are lots of signs that a unitary theory of quantum gravity can be constructed (the AdS/CFT correspondence that links gravitational theories in some dimension to a purely non-gravitational quantum theory on some boundary one-dimension lower provides relatively concrete examples of this).

    One could in fact make the case that the disagreement between two observers as to what is physically going on when one of them falls into a black hole is situation where many worlds may be on a very firm footing. There is clearly a branching since the inside observer can no longer communicate with the outside one, so you could cast this as one of the clearest cases in which the universe “splits”. It’s so extreme that the two observers may not even agree about the concrete physics: one sees Hawking radiation, while the other sees nothing out of the ordinary as she crosses the horizon.

  38. Gravatar of David Kagan David Kagan
    10. February 2013 at 11:21

    Eliezer: Thanks for the link. I actually read through a lot of your sequence some number of years ago—it’s great!

    I get your point: many worlds is not as widely accepted due to a certain amount of historical contingency. While I think that there’s a lot of truth to that, I also think that just as Copenhagen has been “dumbed down” to make it more user-friendly for the masses (of physicists!), the same would probably have occurred with many worlds. For example, I bet a lot of physicists who learn the orthodox interpretation of quantum mechanics in your alternate universe think of many worlds as saying that the universe is branching at every decision point, and they don’t worry so much about issues like the preferred basis problem or the interpretation of probabilities.

    Likewise, there has been a lot of confusion about the Copenhagen interpretation, and to a large extent, the masses (of physicists!) take it to be equivalent to something like “shut-up-and-calculate”. If you’re slightly more thoughtful, you consider it equivalent to the idea that there is a sharp divide between the quantum and classical worlds.

    But if you look at what Bohr, Heisenberg, and that lot actually wrote (not to mention Einstein), they weren’t being fools. I urge you to take a look at Chris Fuchs’ discussion of these topics. He makes a pretty strong case that these people knew that what they really were talking about was an interpretation wherein the wavefunction plays a role akin to a classical probability distribution in a subjective Bayesian approach. From that view, as I wrote above, collapse is just a form of updating one’s knowledge about the world.

    Sure, this leaves a deep puzzle: why does the world demand that the laws of probability are quantum rather than classical? What is that kernel of actual, ontological, physical reality that makes this less intuitive notion of probability the one to use?

    But that’s a pretty grand puzzle to ponder too, no?

  39. Gravatar of genauer genauer
    10. February 2013 at 11:54

    Folks,

    I have a PhD in physics, more on the experimental / engineering side, but I did also have (near) perfect grades in theory. And real world / research experience, something I believe Kagan and Yudkovsky are a little short on. But lets hear.

    Most of this talk here sounds quite bizarre, and I say, just forget completely about multi-world and quantum mechanics, when you want to talk about anything outside physics and chemistry.

    The unique position, physics has today, depends pretty much on making successful predictions, in historically ever increasing scope and precision. If folks say “Newton is wrong”, I cringe. It took 4 years to find one observable situation, in which the Newton prediction could be shown to be off the observation by just a tiny amount, and in agreement with Einstein’s general relativity.

    Here on earth 99% do not even need Newtons law (F =g m1 m2 / r^2), and do not know it, 2 years out of school, and s = ½ g t^2 is sufficient, because
    a) The difference is not relevant
    b) They can not even measure it, and
    c) Other influences like air friction are much more important
    Historically people have so often tried to talk in analogies to the latest results in physics (celestial mechanics, electrodynamics, statistical, QM, QED, to explain stuff in other areas, and most the times just 50, at max 100 years later this just sounded weird.

    There is a very interesting book from a Austrian philosopher, Paul Feyerabend “Against method”, which explains, why Galilei was just gigantically overplaying his cards, what evidence he really had, and how precise this was.

    And foremost he was violating his probation orders, to not claim that his allegations are proven, which they were not at this time, and this at a time, 1632, where half of Europe was hacking the other half to pieces over religious differences. At the end of the 30 years war 1618 – 1648 half of Germany was dead. The last thing you need is some snake oil salesmen like Galilei.

    I wondered how to explain this best to folks like you. Let’s try this:

    a) Has ever any of you actually tried to calculate the static of a house? How many wooden bars you need, to make it stable

    b) Has ever any of you tried to calculate planetary positions? And this without knowing Newtons laws and differential calculus, not to speak of having at least a programmable pocket calculator at hand?

    c) Has any of you ever tried to predict economic growth by Solow’s model , in the real world?

    If you would do a), you would find, that not only for wood, but for steel etc as well, you have safety factors of usually at least a factor of 2, because the individual bar varies, dependent on its making, what you then do to it, get it wet, chemicals in the air, etc. etc. There is no point to get into more detailed calculations of little creaks in the surface and atomic forces between strains of wood, or tiny amounts of other elements in the metal at this level.

    If you would try b) you will find that it is impossible. The elliptic, heliocentric model was more beautiful, but the geocentric much easier to calculate, and in fact both were not done in the way, we would do this now, well, because they would need Newtons equations. (I ll give you an example how some calculate it today: http://www.stjarnhimlen.se/comp/tutorial.html)

    If you try c) you will get mired in a ton of accounting issues, and just extremely lousy fits, if at all.

    Economics will never come even to a precision of only the ptolomaic epi cycle model.

    In physics, electrons behave exactly the same, all of them, all the time, according to relatively simple laws.
    Economics deals with people, conscious actors, of which at least some have some memory, ability to analyze, and change their behavior.
    80 years ago, people reacted collectively with significant lower prices and wages to the depression (30% from 1929 to 1933). What did we do this time? None of this.

    Tell me one economic model, where parameters are known better than 1%, and constant over more than 100 years. Beyond accounting identities.

    Astronomy deals with extremely highly repetitive phenomena, where folks had thousands of years for subsequent refinement of observations over many orders of magnitude.
    Most other stuff, you can make experiments, look at the results, scratch your heads, and improve on the next experiments, where you can control more influences, eliminate others, and measure better.

    Rinse, repeat. Do experiments in ultra high vacuum. Let some gases in slowly, and watch the impact. Build a better scale, a better gauge, a better detector, measure longer. Repeat.

    You simply don’t have this in economics. And you never will.

    Look at the difficulties, we had with the many body problem, to “prove” that this will be “stable”, at least for 3 bodies. Meaning, that our planetary system will be not flowing apart, if some huge asteroid comes in on a strange trajectory.

    On the other hand, with some N= 10^23 particles in one cubic cm, the variation of the mean is just 1/ sqrt (N), way beyond any measurement accuracy and especially beyond any practical relevance in all practical cases.

  40. Gravatar of ssumner ssumner
    10. February 2013 at 13:12

    Mike, So was the Pope right or wrong to tell Galileo to shut up and calculate? Are you saying the calculations were science and the description of reality was philosophy?

    Thanks Neal.

    J. What if the correct price is differnet in different universes? But I do accept your broader point about the difference–the stock market mostly follows classical laws, and it’s mostly about our ignorance due to complexity, not quantum type superposition.

    David, I’m in way over my head, but I assumed that the branching metaphor also applied to the thickness of branches-the thicker the more likely. I had thought they used the term “measure” for thickness—is that wrong?

    Genauer, I’m always amused when people talk about how physics is so much more precise than economics. At equal levels of complexity there is no difference. How accurately can physicists predicts weather 10 days ahead? How accurately can they predict earthquakes 5 seconds ahead. How about big solar flares? That’s all applied physics. Adjusting for complexity, physics is no more accurate than economics.

  41. Gravatar of phil_20686 phil_20686
    10. February 2013 at 13:43

    That is a little bit circular scott, the definition of a complex situation is pretty much exactly one where you cannot reliably predict the future.

    I mean your computer’s processor makes use of several quantum effects and has some 10^26 atoms or so, the only reason we think that is not a complex system is because our explanations are so successful that it no longer seems complex. :)

  42. Gravatar of genauer genauer
    10. February 2013 at 15:01

    Scott,

    which physicist claimed that he/we could do “predicts weather 10 days ahead? How accurately can they predict earthquakes 5 seconds ahead”

    How extremely long did I write here about the nonsense of unwarranted complex descriptions, like QM and multiple worlds, if you are inherently limited to not even understand the simple dependencies?

    Galilei had next to nothing to do with the numerical advances of astronomy. Tycho Brahe, Kepler, Kopernikus. He had other merits, not to be forgotten. But he was a genius in selling, to his own advantage,too.

    A giant grant getter. The way he sold the telescopes of others, Jim O’Neill, Madoff and Corzine would envy him : -)

    But physics has wide areas, where it can and does claim huge precision, like planet positions. Economics not. And I tried to explain, why it never will. Sooo, dont claim it.

  43. Gravatar of ssumner ssumner
    10. February 2013 at 15:37

    genauer, I think you misunderstood my comment. I never said physicists claimed to be able to predict earthquakes. I said physicists cannot predict any better than economists, for problems of equal complexity. And if you aren’t comparing equals, the comparison is pretty meaningless. I could argue that biology is better than physics at explaining animal behavior. So why would anyone care? The fields are completely different. It’s an apples and oranges comparison.

    Surely physicists aren’t so naive that they think it makes sense to argue physics is better than some other field because it can predict eclipses. That’s a simple problem! If you want to impress me, predict the tsunami that killed tens of thousands of Japanese. I don’t care about eclipses. Or silly stunts like sending a man to the moon. Tell me the economic policy that would save millions of North Koreans from hunger. That would be useful.

    phil, Computers are simple compared to the human brain, much less 7 billion brains interacting.

  44. Gravatar of Brian Donohue Brian Donohue
    10. February 2013 at 16:56

    This is brilliant Scott! Maybe you’re not brilliant (tho I’m skeptical), but this is brilliant.

  45. Gravatar of David Kagan David Kagan
    10. February 2013 at 17:37

    Scott, there is a way of thinking of the branches as “thicker” than others, but you have to add that into the many worlds picture as an additional postulate.

    Also, I think I’m in almost complete agreement regarding the relationship between predictability and complexity. Physics gives an air of precision because we deal with extraordinarily simple things. Actually, the key is that in many circumstances, we can rely on a relatively clean separation of scales to help us out. But when processes on many different scales (energy scales or distance scales, whatever you like) all become important, then all bets are off.

  46. Gravatar of Saturos Saturos
    10. February 2013 at 22:47

    Scott, thanks for doing posts like this occassionally, it gets the intelligent “lurkers” to drop in comments and confirm their existence to me, and thus the influence of this blog. And it seems like I did the right thing skipping yesterday’s session, people have made my points better than I would have.

    Don Geddis, no, Scott Sumner is far more radical than David Deutsch. And Scott’s views (or at least his prescriptions) will become orthodox within a decade or two. I’m not sure about Eliezer – his ideas are at once far more mainstream and far more radical…

    Scott, you seem to be pretty oblivious to genauer’s basic point. Physics is far more useful than economics, with far more predictive success. You suggest that this is because their tasks are easier. But even if they are, how does that change the fact that physicists are successful in a way that economics are not? And then why shouldn’t we say that physics is successful while economics is not? (Of course economics has some success, but tiny compared to the amount of ‘knowledge’ that physics has given us.)

    “Tell me the economic policy that would save millions of North Koreans from hunger.” It’s probably going to involve some applications of heat, light and electricity, though…

    P.S. Hitler’s paintings were better.

  47. Gravatar of genauer genauer
    11. February 2013 at 04:36

    Sarturos,

    thanks for pointing out the overwhelming volume of precise predictions Physics can make nowadays.

    And I want to add, that most of this developed only the last few hundred years. It goes closely together with the advances in productivity, we had in the European culture (that includes you in those 13 colonies : – ), coming out of the dark ages, when we were not only behind, but did collectively forget stuff, we already knew, like Eratosthenes (wiki it!) earth as a ball and calculating its circumsphere. I am still not sure, that we “really” understand this European explosion (errrm, just 2% per year, folks), but it is a very interesting topic for how we can make sure that this continues, now with the significant participation of the other cultures (Sino, india) again as well.
    And I enjoy presently reading Deidre McCloskey “Bourgeois Dignity, why economics can’t explain the modern world” addressing a pretty systematic list of them.

    One more point, I really want to drive home with you, especially with physical “laws” are nearly never “exact”, but

    1. APPROXIMATIONS.
    Galileis s=1/2 g t^2 is a very good approximation of the 1/r^2 Newton law on earth, and Newton is a very good approximation of special relativity, and so on.
    Galilei is NOT wrong, because Newton came, and Newton not because of Einstein, …

    Just one more example, and I actually checked this against the various versions of “Formelsammlung” I had at which time (there is no English wiki!, something always interesting,
    Question to Kagan: your word, and what did you have at what education age? !!),

    The simple “ideal gas” equation p V = n R T, good enough to be taught until 12th grade, and the vast majority of normal life considerations. At university you learn the van de Waals “real gas” equation (p + a) (V – b) = n RT with a and b small Terms in most cases. And when you then go on to what is going on in the Sun, it gets more complicated, and so on, the USUAL situation in physics, NOT the exception.

    Most the times I could go on with additional comments and add-on terms, until people cry uncle / for mercy. Most of the times the lowest order approximation is absolutely enough, for PRACTICAL purposes.

    2. EMPIRICAL , engineering rules come nearly always before the theoretical explanations

    a) Sze “Physics of Semiconductor Devices”

    b) Jackson “Classical ElectroDynamics”, Goldstein “Classical Dynamics”

    c) Mas-Colell “Microeconomic Theory”

    When I look at a book like a) Sze “physics of semiconductor devices”, LEADING EDGE in this, 40 years ago, I see hundreds of plots, carefully crafted with precise axis descriptions, units, numbers, experimental points, and model, and theory curves through them. Some of them with just 3 points per curve, when that curve is simple linear in the right way to plot it. Many more points, if things are more complicated.

  48. Gravatar of The Apple Pie Theory Of Distributional Economics « squarelyrooted The Apple Pie Theory Of Distributional Economics « squarelyrooted
    11. February 2013 at 06:10

    [...] Now, a great calamity happens – but to whom? A quantum event happens, splitting our nice universe into parallel universes: [...]

  49. Gravatar of David Kagan David Kagan
    11. February 2013 at 06:11

    Saturos, I think that Scott already addressed your question. Namely, he said that he thinks you shouldn’t compare things when you don’t have an equal base of comparison. First of all, economics is a very wide-ranging field of study. There are some extremely impressive results in various areas of microeconomics (perhaps not as precise as physics, but still, robust, repeatable, etcetera). So when we are discussing the inadequacies of the field, we’re probably talking about macroeconomics.

    But the point is that there are some pretty major complications stemming from the interactions of entities on many different scales in macroeconomics. These lead to rather unintuitive phenomena (e.g. think of the fallacy of composition: everyone tries to save, so nobody is able to).

    Then of course there’s the problem of running experiments with a macroeconomy! So they get it at both ends, the theoretical and empirical!

    When physicists deal with systems that are complicated in this fashion, they also have a hard time with prediction. I’d say that we still are at an advantage because the basic building blocks we have access to (and the ones that are useful depend on the problem at hand) are all pretty simple and well understood, so we can often make a bit more headway, even in dealing with complex systems (like the climate, for instance). See for example the development Genauer describes regarding modeling fluids, first via the most idealized equation, then gradually building in the complexity to deal with something like the Sun.

    But I think Scott’s basic point stands for the most part. As one of the previous commenters mentioned, it’s even almost circular. Complexity makes prediction and precision hard.

    Genauer, I don’t think anybody here is disputing the notion that at large enough scales, Newtonian theory (and even various simplifications of it) is an extremely good approximation to the way things work physically. I doubt any serious quantum field theorist would argue with that (the renormalization group is basically the codification of this insight). The many worlds discussion was a discussion about the nature of quantum mechanics, which I think you’ll agree, underpins pretty much our entire understanding of physics (except for that pesky force of gravity). When you are trying to understand a question of that sort, you have obviously have to talk about quantum mechanics in all its glory. The approximations don’t cut it.

    To take another example, spacetime for most circumstances that “practically” matter to us is pretty flat. But if you want to understand the deeper nature of spacetime, you need general relativity—not its Newtonian approximation.

    Since you asked—at least, I think you asked—I’m part of the physics faculty at the University of Massachusetts in Dartmouth. I was a postdoctoral fellow at Columbia University (my main collaborator there is Brian Greene). My Ph.D. is in theoretical physics from Cambridge (UK), and my undergraduate degree is a double major in math and physics. I’ve not done much experimental work, but I did very well in my physics labs.

  50. Gravatar of Eliezer Yudkowsky Eliezer Yudkowsky
    11. February 2013 at 08:22

    David, if you’ve already glanced in at my quantum mechanics posts, then you already know that… no, wait, that was several years ago, it’s totally unreasonable to expect anyone to remember all that stuff. So just to quickly restate for the purposes of reminders:

    1) Of course I know that Deutsch, Wallace, and many others think it’s possible to derive the Born statistics from decision theory; I said outright that I thought this was madness (you can’t make different outcomes more probable by caring about different things).

    2) I do think that Hanson’s mangled worlds is a promising approach, and more generally I suspect that an explanation of the Born statistics should arise from the unitarity of quantum mechanics, since unitarity means that the amount of metaphorical ‘causal matter’ (ability to dominate amplitude values in parts of the wavefunction) is conserved and proportional to the integral of the squared modulus, in other words, our probability of finding ourselves in the part of a wavefunction is going as something like the amount of ‘causal fluid’ in that wavefunction. Collapse interpretations make no use of unitarity – we could just as easily be eliminating branches proportional to the third power of the modulus.

    3) More generally, no amount of single-world interpreting gets us any closer to understanding the Born probabilities. Why say that the mysterious force munching off parts of the otherwise continuous wavefunction is eliminating all but one world? Why not leave behind a population of worlds? Why should there be just one Bohm particle guided by the wavefunction instead of a population of them? Above all, how is it any better to ‘provide a mechanism’ for the Born statistics by saying, “There is a mysterious all-but-one-world amplitude-eater which operates according to the Born statistics” vs. just saying “Here are the Born statistics”? It seems exactly like saying that you need to ‘provide a mechanism’ for the electrical field by saying that there are little angels pushing on charged particles, and the electrical field tells the little angels how to move.

    4) That the wavefunction is an epistemic description of our uncertainty about some deeper, locally causal, single world is decisively ruled out by Bell’s Theorem. I can’t quite say that everyone knows this part, but everyone knows the math and I think a majority of physicists would agree with what I just said, though they might phrase it differently since they wouldn’t be acquainted with Judea Pearl’s standard definition of local causality which is more something that probability theorists know.

    5) The case for many-worlds has never rested on the collapse interpretation making different predictions from many-worlds – albeit many possible thresholds of collapse have been tested and already falsified. Rather, it’s just that many-worlds are what you get if you apply the same description at all levels of the theory; and trying to eliminate portions of the wavefunction to arrive at a single world requires introducing an extra law which not only receives a complexity penalty according to standard probability theory, but also introduces the only non-differentiable discontinuous faster-than-light CPT-irreversible non-linear non-unitary acausal informally-specified process in all of physics. Collapse isn’t a physical theory, it’s magic. Anything that eliminates distant parts of the wavefunction and leaves behind a single world will be equally magic.

    6) Issues of preferred basis are illusions of representation; it’s like demanding of Special Relativity that it give us a preferred meterstick or demanding of Newtonian mechanics that it give us a preferred direction of north. There’s a genuine puzzle in the Born statistics, but the underlying facts about causal processes (in general, and carrying out cognition in particular) are invariant with respect to changes of basis; this is no more a difficulty for many-worlds than for any other physical theory. This arises as a misunderstanding only if you think that ‘worlds’ are fundamental or new ontological elements of MWI, but that’s like thinking ‘planets’ are a fundamental element, aside from atoms, of Newtonian mechanics. MWI is just the theory that the wavefunction is real and that its mechanics solely constitute the causal processes of reality and our cognition within it; plus there is an unexplained mystery of the Born statistics, to which MWI as a whole says ‘hypothesis non yet fingo’ (i.e., we don’t yet know). Other interpretations of quantum mechanics add further strictly unnecessary postulates, expand the ontology a la Bohm, or throw on wildly confusing non-objective bad amateur epistemology a la RQM which is just MWI in denial, etcetera. Occam’s Razor slaughters all of MWI’s opposition without hesitation.

  51. Gravatar of Doug M Doug M
    11. February 2013 at 09:42

    Mathematics is the “Queen of the Sciences.” And mathemeticians don’t use the scientific method, either.

    Suvy, phyisicists uses power law distributions to describe all sorts of phenomina.

  52. Gravatar of Neal Neal
    11. February 2013 at 10:01

    J: I am aware that there are no hidden variables in (classical) QM. I don’t mean the analogy to extend so far as to suggest otherwise. Although (I think) it’s epistemically interesting to contemplate whether, from the perspective of the economy, any event that has not affected markets can be said to have occurred.

    *****

    I am a little bit confused to see laws of probability invoked in the context of quantum field theory, because I’m given to understand that the relevant path spaces don’t admit integrals. Feynman integrals don’t make any mathematical sense (hence don’t make any sense in the context of probability theory) – they just *work.*

    Admittedly, I don’t work in gauge theory, per se — I’m just going by what I’ve heard geometric topologists say.

  53. Gravatar of Neal Neal
    11. February 2013 at 10:02

    Doug, mathematicians don’t do science. :) We look at internally consistent systems. It just so happens that we appear to live in an internally consistent universe, and some of these systems are useful in generating predictions about that universe.

  54. Gravatar of Suvy Suvy
    11. February 2013 at 10:18

    “Suvy, phyisicists uses power law distributions to describe all sorts of phenomina.”

    This is true; much of the phenomena in the real world scales and thus follows some sort of a power law distribution. In fact, it could be argued that power law distributions occur more often than normal distributions do. Either way, power law distributions can be used to describe winner take all effects and are much more practical in economics/finance.

  55. Gravatar of David Kagan David Kagan
    11. February 2013 at 13:04

    Hey Eliezer! Thanks for the very detailed response. I’m thinking that maybe we shouldn’t drive people crazy discussing this on Scott Sumner’s blog, so perhaps we should go over to e-mail? Which of course raises the issue of how to find each others’ e-mails.

    (of course, I’m happy to continue here, I just thought it would be courteous to suggest an alternative).

    Neal: Not sure what you mean by “classical QM”. Do you mean vanilla QM without any overt interpretations laid on top of it? Because there are hidden variable interpretations of QM (Bohmian mechanics being the best known example). The key is that the variables end up being non-local.

    Probability abounds in anything related to quantum theory, at least when you want to confront it with experiments. We don’t predict the motion of particles, we predict the statistics of them being prepared in some initial state and ending up in some final state (the state here can refer to position, momentum, or something else).

    The Feynman integral is a prescription for doing calculations of this sort in the quantum theory of fields. I think saying it’s undefined is a little too quick. It’s probably better to think of it as needing to be defined in any given problem that one is considering. In many cases, this typically means making some sort of finite approximation (such as lattice gauge theory). However, there are some really lucky situations where the Feynman integral becomes tractable. Typically, these are systems that exhibit a tremendous amount of symmetry and that effectively render the space of paths that you integrate over almost finite (for example, the contributions to the value of the integral come from a discrete set of paths, or equivalence classes of paths).

    I’d say that there’s probably a cultural divide between mathematicians and physicists with regards to the path integral, but a useful rule-of-thumb is that where there are concrete results that emerge, assume that the integral in that situation has been defined sufficiently well for producing those calculations.

    However, even the symbolic, general form of the path integral can be a very powerful tool for reasoning about lots of systems.

    I’d be happy to discuss this in a more detailed manner, but I’m not sure if people would be happy to see me do that!

  56. Gravatar of Scott Sumner Scott Sumner
    11. February 2013 at 13:49

    Anyone, This is probably a stupid question, but assume some a quantum computer did some super hard math problem, something that a normal computer as large as the universe would take a trillion years to solve. I know that we are a long way from that, but I infer from the debate it would provide no support for the MWI, even if possible. That’s because everyone keeps insisting the MWI is not testable. So to the critics of the MWI, if a quantum computer did that complex puzzle solving–and didn’t use other universes, do you have a sense of the “reality” out there where this computation was done? Apologies if this is a stupid question.

    Thanks Brian, but I think you’ll see more brilliance in the comment section here.

    Saturos, I’m positive you are wrong about Hitler’s paintings, and I’m pretty sure you are wrong about physics. One can make any sort of “importance” claim one wishes. For instance “My garbageman is far more important than my brain surgeon, because modern sanitation has saved far more lives than brain surgery.” Yes, that’s true in a sense, but in another sense you are comparing apples and oranges. Most people would say it’s absurd to claim the science of garbage pickup is somehow more impressive than the science of brain surgery. My point is that we should compare apples with apples. Suppose both economics and sociology claim to explain crime. Economists claim it’s all about costs and benefits. Sociologists claim that poverty causes crime. Then the 1960s happen, punishment gets much weaker, and poverty plummets, and crime rates soar. It looks like the economists were right. In that case, if they were both trying to explain the same phenomena, then you might make a comparison between two fields. Or you might see who’s paid the most, and assume that represents marginal products. Or any other arbitrary comparison. But when people claim physics is somehow more “precise” then economics they are simply making fools of themselves–you can’t compare the fields unless you are evaluating problems of equal complexity, and then the physicists do no better.

    Tell me which art form is better; novels or painting or opera? Which fruit is better, apples or watermelon? Which country is better, France or Germany? Italy or Norway? Which field is better, chemistry of biology? Now tell me once more, which field is better, economics or physics?

    I’d much rather live in a country that had no knowledge of modern physics, but good economic policy, than say North Korea (bad economic policy), even if the North Korean schools were full of accurate teaching of physics.

    Sorry if this sounded like a rant–I am actually a pretty big critic of econ, as you know–I just find these sorts of comparisons to be pointless.

    Hitler’s paintings are more “realistic” but Bush’s are far better—it’s not even close. That’s a comparison I am very comfortable making.

    Genauer, At least we both like McCloskey.

  57. Gravatar of David Kagan David Kagan
    11. February 2013 at 15:00

    Scott, you should really bone up on your quantum mechanics. It can only help you in your quest to get NGDPLT to be totally mainstream. Bernanke and Krugman will respect you more.

    I joke of course.

    (Although I think that if they don’t, Bernanke and Krugman *should* respect you more, regardless of your prowess at quantum theory!)

    You ask an excellent question. Indeed, there’s an MWI interpretation of such a problem, but MWI is also a bit misleading if you take the most intuitive approach to it (Warning: we are getting outside my area of expertise here—I’m not a quantum information theory guy). To run a quantum computation you have to initialize a quantum state in some desired fashion. You typically have to maintain some system in a very delicate superposition of states—it’s delicate because without a high degree of isolation, the local environment will measure your system for you and spoil the coherence of the state, ruining your computation.

    You set this thing up somehow, and you can implement various transformations of the state that maintain the coherence of the system.

    At the end of the process you do a measurement and get a definite outcome. In fact, the probability of getting the right outcome is typically less than 1, but by repeating process many times you can pick out the right answer with high certainty.

    Okay, so where would MWI say the parallel worlds come in? Well, they sort-of show up when we set up the superposition of states. But the entire point of the quantum computer is to keep that superposition isolated—basically, you don’t let the worlds “grow” and “split”. Eventually, you do perform a measurement, so you could say that at that end stage in the computation the universe starts to “unzip”, but the computation was done *before* the uncontrolled unzipping happened.

    In fact it’s crucial that the unzipping doesn’t happen until the end because otherwise it becomes very hard for the universes to interfere with one another, and it is the interference effects that the algorithms capitalize on.

    Anyway, the point is, the whole parallel computing metaphor is useful on the one hand, but as usual, treacherous on the other.

    An alternative is to simply say that systems in Nature are imbued with many more possible states than we typically see in our classical view of the universe. Quantum computation exploits these exotic (to us) states in a manner that allows us to enhance certain (not all) types of computations. From this perspective, the answer to your question is rather straightforward. You ask “where is this computation taking place in reality?” And the answer is simply, right here. REALLY!

    I just want to make clear, I’m not an expert in quantum computation—it’s just something that I’ve read about a bit. If anyone knows more, and if I’ve made some grievous error in my explanation, please do correct it. The last thing I want to do is confuse people with wrong information.

  58. Gravatar of Neal Neal
    11. February 2013 at 15:42

    David Kagan-

    First, I hope you and Eliezer continue discussing in public. I’m quite enjoying the read.

    To reply to your response to me, I’m using “classical” to distinguish non-relativistic QM from QFT. (I have Schrodinger’s equation in mind – I have no knowledge or intuition of Heisenberg’s approach.)

    Anyway, in classical QM, where particles are curves in L2, we can make mathematical sense of the statistical interpretation. An observable is some self-adjoint operator; the associated probabilities are norms of projections of states onto eigenstates of the operator in L2, etc. Functional analysis provides a nice, rigorous framework for this.

    In QFT, where particles are (I don’t know what), I’m told that the relevant measures are known to not exist – there is no known way to make mathematical sense of path integrals.

    (Obviously, they *do* make sense, since they generate such fine predictions, but the rigorous mathematical description hasn’t yet been invented.)

    In limited situations, where mathematicians have made sense of some forms of calculating the path integral, they’ve made tremendous strides (for example, Reshitikhin-Turaev field theories). But in general, mathematicians haven’t yet been able to develop a framework that rigorously describes quantum fields – from their perspective (the cultural divide, as you allude) a lot of the physics is voodoo symbol-pushing: “Multiply by infinity and divide by zero, and hey, predictions to 0.00000000001%”.

    Again, this is from conversations with mathematicians who work with gauge theories on 3- and 4-manifolds. I’m no expert in the matter. All I mean to say is that treating QFT as obedient to the laws of probability seems wrong-headed to me, because QFT is in general still beyond the reach of mathematics.

  59. Gravatar of David Kagan David Kagan
    11. February 2013 at 18:19

    Neal, I’ll count you as a vote for continuing to pollute Scott’s blog with things that probably only show up in economics in another branch of the multiverse.

    Regarding path integrals, I think you and I are mostly in agreement. The cases of qft’s that have a very well-defined path integral treatment are 0+1 dimensional (i.e. ordinary, non quantum field theoretic quantum mechanics—and even there, I’d bet it’s only for some subset of Hamiltonians), and so-called topological quantum field theories (although conformal field theories are a borderline case where a lot about the path integral can be recast in terms of certain operator algebras. In 2D, I’d add certain quantum integrable models).

    Sadly, the basically well-defined cases are so special that they don’t capture most aspects of realistic physics (but I still think they shed light on the nature of quantum field theory).

    I completely agree with you about where mathematicians are at regarding the path integral in general—in fact, I think I was basically saying the same thing. I have some math friends who are always bugging me about this. The physics response of course is, “hey, we can calculate the anomalous magnetic moment of an electron to a precision of 11 significant figure so I guess you math guys better get your act together!”

    Honestly, when you’re a physics grad student, you also feel like there’s a certain element of voodoo symbol pushing going on. But eventually, you start to understand things like the renormalization group and the need for a cut-off in any theory other than quantum gravity (or maybe that too? Who knows?!), and you realize that the Feynman integral in realistic physics is a scheme for organizing various approximations as well as revealing certain non-perturbative aspects of your theory.

    I think that the stuff going on connecting QFT to various topological properties of manifolds is truly exciting stuff! But I think that the general idea of finding a rigorous way to do the path integral is misguided if it doesn’t take into account the fundamental role played by renormalization and the scaling properties of theories.

    So I come back to where I started—we’re clearly on the same page about this stuff.

    P.S. Renormalization group is not actually a group—I believe it’s technically a semi-group, but my recall of math jargon I read about in grad school is a bit rusty.

  60. Gravatar of Phil Phil
    12. February 2013 at 05:23

    My understanding is that witten broke field theory when he constructed a well defined perturbative two dimensional quantum field theory with nice perturbative interactions and then demonstrated that the path integral was everywhere and always identically zero. At the very least it tells us that we do not understand at all what constitutes a well defined QFT.

    Quantum computing is confusing because there appears to be no theoretical reason why I doesn’t work. But if it does work you can rapidly build a computer with more computing power than there is entropy in the universe, which intuitively feels impossible. Obviously intuition can be wrong, but it appears that a working quantum computer likely breaks the laws of thermodynamics, (where does all the entropy go when you turn if off?) which are already proven for CPT invariant field theories via unitarity which implies the transition matrix doubly stochastic hence second law.

    Particles are simply the natural interpretation of a field theory that is sufficiently perturbative so as to be considered as interacting locally between conserved packets. Strongly coupled field theories like QCD no longer have particles in there strongly coupled limits. Similarly curved space acts constantly to evolve the packets and hence ‘creates’ particles, but really particles are just a special case of fields having local conserved packets.

    Scott, mwi means one of the three different things. Group one believes its never/not imminently possible to test. Group two believes either that it has significantly better explanatory power, or that some unique interference is possible which makes a test. That is that universes interfere even after branching in a prediction separate from QM.

    The easiest way to think about why gravity is non renormalisable is to note that the gauge symmetries of qed preserve the loop order. That is if I take a single Feynman diagram and do all the gauge transformations to built a gauge invariant quantity, I always preserve the loop order. So I can talk about a gauge invariant quantity at loop order one, or two etc. in gravity, if I draw up some effective field theory and draw a diagram and do a symmetry transformation I get a diagram with a different number of loops. Hence perturbative expansions can never preserve general covariance. Now this doesn’t necessarily matter, but summing infinite series is v hard. Ads/CFT gets around this by reordering the sum in a way that is easier to do. There is something very important in this correspondence that we do not really understand.

  61. Gravatar of ssumner ssumner
    12. February 2013 at 06:13

    Thanks David, That’s very helpful.

  62. Gravatar of David Kagan David Kagan
    12. February 2013 at 06:33

    Phil—let me work backwards.

    I agree that there’s a lot we don’t understand about AdS/CFT. Part of what makes it so difficult is that the correspondence links a weakly coupled theory to a strongly coupled one, so when we are in the regime where we can apply standard techniques to say, the CFT side, then we cannot simultaneously do calculations on the gravity side, and vice-versa.

    That said, there has been enough work on it at this point that the various examples of the correspondence are pretty concrete. People are now exploiting it to study things like superfluids and superconductors. It’s certainly the closest string theorists get to making contact with physical systems that are realizable in the lab (note: that hasn’t quite been achieved yet though).

    I think what you say about loops in a gravity theory is interesting, but I actually think that seeing why gravity isn’t renormalizeable is easier than this. Unlike electrodynamics, the coupling constant in gravity has units. It scales like a mass-squared, i.e. like an energy. In these sort of situations, if you do calculations at energy level E1 and you regulate all the divergent terms and do the relevant experiments to measure the values of the new couplings you had to introduce, and then you go to a higher energy scale E2, then you have to do the whole thing over again. Basically, there are an infinite number of new bits of data you need to go out and measure in order to calculate with the theory at all energy scales. It’s just the standard reason that non-renormalizeable theories aren’t renormalizeable.

    Gravity is weird in that it appears to suggest its own cut-off, namely, where you start probing energies that spontaneously generate microscopic black holes. That’s a different way of arguing that something funny is going on with gravity.

    Regarding MWI: Decoherence only exponentially suppresses the interference between the different branches, so in principle (maybe), you could run an experiment that tries to see the effects of this interference. So people talk about trying to put larger and larger objects into odd superpositions (Anton Zellinger did it with a virus I think!).

    The thing is, I don’t think that this distinguishes MWI from any other interpretation that refrains from doing violence to the mathematical structure of quantum mechanics. You could concoct a non-local hidden variable theory (and not all of these need to be as ontologically scary as Bohmian mechanics) and get the same results. There are even interpretations that assert that we should read quantum mechanics as saying that the future influences the past—but in precisely such a way as to ensure that information flow is always causal. These are so-called retrocausal interpretations.

    MWI has no monopoly on interference effects, so I’m afraid I personally wouldn’t be converted, even if someone could put my brother’s pet rabbit in a superposition (without harming it of course).

    I like your explanation of particles as being just one way to look at certain limits of a quantum field theory. I think that’s pretty much accurate. Regarding strongly coupled QCD, what’s cool about that is that in that regime we know what happens—the particles that are in the fundamental description at high energies lose their distinct identities and they form bound states that basically are the fundamental degrees of freedom of the lower energy effective theory. These bound states are protons, neutrons, pi mesons, etcetera.

    What’s really funky is the fact that you can construct theories that appear to have one set of fundamental particles that collectively give rise to particle-like bound states and then find dual theories where the bound-states from the first theory become the fundamental particles and the fundamental particles from the original theory become the bound-states. I personally think that even the mathematical possibility of such models is telling us something deep about the limits of “fundamentality”. But I only have some vague ideas about what at this point it all really means.

    Quantum computing does not defy the 2nd law of thermodynamics. It’s not magic! In the end, the computing power of a quantum computer is not too much different from the computing power of a classical computer (sorry guys!). Yes, there are *certain* classes of problem that can be solved much more rapidly. But it’s believed that you’re not going to be able to reduce NP problems to P (believed, because even given the quantum nature of these computers, people still cannot prove that either P=NP or that P not = NP, but most computer scientists think that the latter is true). I highly recommend checking out Scott Aaronson’s blog and website. He’s one of the leading quantum computing theorists out there (he’s at MIT), and his prose is really fun to read.

    I’m not sure what you mean when you say that Witten “broke” field theory. If anything, Witten dramatically enhanced our understanding of quantum field theories and their connection to geometry. He constructed quantum field theories that are capable of computing knot invariants, topological invariants for 3-manifolds, and he showed how these things connect to physical concepts like supersymmetry. There is nothing broken about these field theories. In fact, they are some of the best defined ones out there!

    He’s continuing to push the boundaries of this kind of reasoning by using QFT to generalize the Jones polynomial (that can be used to distinguish different types of knots). He even came out with a fun but perplexing paper a couple of years ago (which I presented to our journal club at Columbia), in which he proposed a clarification of the Feynman path integral with an eye toward applying it to these geometrical problems.

    Incidentally—just to plug for string theory—much of the work Witten has done has very natural connections to string theory (no, not because it’s about knots!). Many of the QFT’s that he’s constructed naturally incorporate supersymmetry and they have natural string theory interpretations. It’s one of the reasons people who work in the subject are so convinced that it is on the right track.

    Ironically of course, all these mathematical advances haven’t given us the tools for extracting the details about the structure of our world from string theory. I believe that we can do it (that’s why I work on the stuff), but I admit that at this point the jury is still out.

  63. Gravatar of Saturos Saturos
    12. February 2013 at 07:00

    Scott, are you disagreeing that physicists have been far more successful at doing what they set out to do (explaining what they set out to explain) than economists have been at theirs? Don’t you agree that a physicist from 1800 would be far more proud of what his field had achieved in the subsequent two centuries than an economist would? (Of course I’m not claiming that physicists are personally superior to the economists, it is due to the limitations of what they are studying.) Why doesn’t that allow me to say that physics is better than economics, just as economics is largely better than sociology? (In fact it’s worse for sociology, since these days we agree that they are largely trying to explain the same things as economists are.)

    I think Hitler’s paintings are far more uncommon and expressive than Bush’s. And I say that as someone who generally prefers modern art. Try this one, for instance: http://i.telegraph.co.uk/multimedia/archive/01121/hitler-painting_1121446c.jpg
    or this one: http://www.ynetnews.com/PicServer2/20122005/900510/LON106_wa.jpg

    Look at the Wikipedia page on Hitler’s art – under “Critical Analysis” you read, “Some thought Hitler’s painting skill was poor; for example because he did not paint people, the cause of which is speculated by LIFE as either his unwillingness or lack of skill. His paintings are preoccupied with architecture such as deserted places, buildings, and farmhouses.” So basically, just brimming with mood affiliation to come up with whatever excuses. He’s very underrated.

    Bush’s paintings are good too, of course, just not as good. I can see paintings of that standard at any common gallery.

  64. Gravatar of ssumner ssumner
    12. February 2013 at 10:02

    Saturos, You said;

    “Scott, are you disagreeing that physicists have been far more successful at doing what they set out to do (explaining what they set out to explain) than economists have been at theirs?”

    Perhaps, but that has no bearing on what we were debating. I’m sure my daughter has mastered the ability to count to 10 much more completely than I’ve mastered economics. What implications do you draw from that fact?

    You said;

    “Why doesn’t that allow me to say that physics is better than economics, just as economics is largely better than sociology?”

    As I said in my post, economics can only claim to be superior to sociology if we can better explain phenomenon that both fields study. Otherwise it’s just apples and oranges. Unless you are greatly impressed by people who can count to ten, I can’t imagine you really believe that accuracy in doing a chosen task is the criterion for success.

    It’s hard for me to evaluate where you are coming from because you didn’t respond to the questions I posed. So I have no idea what you mean by “better.” If you could tell me whether Italy or Norway are the better country, I’d get a better sense of where you are coming from.

    I’ll admit that those paintings are far different from the Hitler paintings I’ve seen. But they still don’t do anything for me–although I suppose one would have to see them in person.

  65. Gravatar of Mike Rulle Mike Rulle
    12. February 2013 at 16:42

    Scott

    This is one of my favorite posts—do not know why.

    The Pope, who I believe was a childhood friend of Galileo, basically told him to shut up—–without the “just calculate” part. He should have let him calculate. I start out with the assumption—which admittedly is just that and no more—that in 500 years we will know more about the universe than we do today. Apparently we cannot (i.e., field of Physics) square the successful predictions made by QM with a “common sense” or “story telling” interpretation of its meaning. I am perfectly comfortable the idea that it is possible (actually, likely) to have a great predictive theory (Ptolemaic predictions were better than Copernicus for quite some time until Kepler got a hold of Brahe’s data) that may not portray the world “as it is”.

    And I certainly enjoy reading about trying to make common sense out of observations which seem impossible. Schrodinger made a great point, however, with his satirical “dead cat” metaphor. He was of the shut up and calculate school. But as a species we will always seek wholeness, with everything consistent with everything else. I think that is a different endeavor than science per se, but more like philosophy (or metaphysics). I think it is great that people have multiple world theories. But it is not (yet) science. It is math combined with metaphysics in a non-contradictory form with science—-but not science.

    Big Bang, on the other hand, is science combined with math and metaphysics. But do I LITERALLY believe in Big Bang? Don’t know. My understanding is that the Math of Big Bang is basically a limit—that it is virtually impossible by probability (if not out right impossible) for us to exist. Yet here we are.

    Big Bang is a wonderful “common sense” description of what happened. It tells a story. We have no such story in QM. So we have multi-worlds invented. All of this is great stuff—-but we want to take our theories too literally, I believe. (Because the “stories” change as we learn more). The theory of relativity at its extremes “make no sense”—just like QM “makes no sense” (think Schrodinger). But they are practical.

    As an aside, I find trying to “tell a story” with physics at least as strange as religion—yet, as I said before, here we are.

    Economics, in my opinion, is just as “strange” (i.e., fascinating) as physics and religion. We do not understand why we are what we are as a species. We do not even know what we are. I think the concept of Hayekian price discovery is a great story and a mystery. I think the fact that humans have always had “money” is a mystery. I think mathematical macro models are funny.

  66. Gravatar of David Kagan David Kagan
    13. February 2013 at 03:30

    Hi Mike,

    This is a really fun post! Although, at this point I’m so committed to this comment thread that I am an unreliable judge.

    Interestingly enough, I just read a nice New Yorker article about Galileo. Apparently the Church gave him the following option: go ahead and do your work, but never claim it as fact. Talk about it only as speculative. They were basically willing to let him go ahead and do his stuff so long as he towed the line on Aristotelian physics as the *fact* of the world, while his insights and observations were just speculation.

    Obviously, that didn’t go over too well!

    You wrote: “I am perfectly comfortable the idea that it is possible (actually, likely) to have a great predictive theory (Ptolemaic predictions were better than Copernicus for quite some time until Kepler got a hold of Brahe’s data) that may not portray the world “as it is”.”

    I’d say I hold the reverse view: I am willing to believe that the world “as it is” does not have to conform to our notion of a good story. This doesn’t mean we shouldn’t try, but I think that ultimately, we have to broaden our notion of what is an acceptable picture of reality. This has happened before when theoretical advances (along with their empirical support) pushed us away from viewing time and space as independent. I’d say it happened when Copernicus, Kepler, Bruno, and Galileo pushed us toward a conception of the universe where we were no longer at its physical center.

    Schrodinger was actually pointing out what he took to be the absurdity of some seemingly naive implications of quantum mechanics. The poor cat was meant to illustrate a seeming paradox: that we never, ever see such a thing in a state which somehow is indefinite about the cat’s aliveness or deadness.

    But the same can be said in a less dramatic fashion about the “here-ness” or “there-ness” of large objects. We always seem to see them in more-or-less definite positions. Yet we have experiments that are able to measure the effect of de-localizing atoms (i.e. making their position indefinite). And we’ve even got experiments that essentially do the same to modestly large molecules (like Carbon-60).

    As such experiments get to larger scales, it becomes continually less reasonable to think of Schrodinger’s cat as paradoxical. Instead, the lack of such cat’s is most likely due to the fact that interactions with an external environment tend to spoil delicate quantum effects, and a cat is very very hard to isolate from the environment.

    Regarding the Big Bang: I’m not sure exactly what you’re referring to, but it sounds like you’re saying that the big bang, and the subsequent properties of the universe we live in are incredibly unlikely. The rigorous version of this argument involves looking at entropy and the 2nd law of thermodynamics. Entropy can be thought of as measuring how disordered a system is. The reason it tends to increase is because ordered states are vastly outnumbered by disordered ones, so walking around state space typically takes you from more ordered to less ordered situations.

    But here’s the crazy thing—the laws of physics don’t have (much of a) preference about which way time is flowing. If you reverse the direction of time in the equations we take to be fundamental, you will find symmetry (mostly—there are some very very very tiny effects that break this symmetry a little bit, but not enough to account for the rest of my story).

    What this means is that, generically randomly walking around the states of a system with time going forward will typically take you to more disordered states. But doing so with time going backwards *also* takes you to more disordered states.

    That is, it’s not only likely that entropy should increase into the future, but for some kind of “generic” time evolution, it seems like it should be bigger in our past as well!

    The only way around this is if the state that we’ve evolved from in the past was more ordered, less disordered, than the state we’re in now. But if you run this reasoning all the way back to the big bang, it would lead you to believe that the state of the universe that gave rise to the bang was so *incredibly* ordered that it was an extraordinarily unlikely state to be found in in the first place. It represents a huge amount of “fine-tuning”.

    Honestly, what this tells me is that we don’t fully understand how to reason about entropy and cosmic evolution. There are lots of subtle assumptions going into the story I’m telling above. This is still an open problem in theoretical physics.

    And that’s the thing: we’re obsessed with telling stories, but really what we’re confronted with are koans and puzzles. When we push our reasoning far enough in any direction, we tend to find that there’s a lot more that we need to try to understand.

  67. Gravatar of Saturos Saturos
    13. February 2013 at 03:59

    “I’m sure my daughter has mastered the ability to count to 10 much more completely than I’ve mastered economics. What implications do you draw from that fact?”

    That learning to count to ten is a more productive enterprise than economics.

    I’m sorry; I’ll leave the rest of this thread to the smart people now.

  68. Gravatar of Saturos Saturos
    13. February 2013 at 04:02

    Put it another way – is the social value added of economics greater than its opportunity costs? Or would many of our great economists be better reemployed as mediocre physicists, from a social planner’s point of view?

  69. Gravatar of Phil Phil
    13. February 2013 at 06:50

    Kagan, what you said about gravity and counter terms is exactly what I said, it’s just that every counter term has an associated loop diagram! When you do RG you are basically going term by term along a series of diagrams and adding a second diagram (counter term) which cancels the divergence. Since all physical quantities must respect the symmetries it only makes sense to talk about using the RG when I have first collected a group of diagrams that as a whole respect the symmetries. This is exactly what we have failed to do for gravity. A two loop diagram in an effective field theory for gravity does not respect covariance. Thus, the RG procedure starts to generate the missing diagrams. This is doomed to fail but it is not that the renormalisation is broken, though it might be.

    On a related note, I have long held the intuition that dimension full constants just represent physics we don’t understand yet. Think of the fermi constant in fermi theory.

    When it comes to gravity and field theory I believe that we are doing it wrong! In the same way that the massless limit of massive qed is not the same as a massless qed, suppose that QFT on flat space is different from QFT on a de sitter space in the limiting case of flatness. I believe there are some people working on this, but the poincare group is very special for building one particle states, and the explicit breaking of time symmetry brought about by de sitter space is a complication. But still, perhaps one day we will manage.

  70. Gravatar of genauer genauer
    13. February 2013 at 08:04

    I wondered how I can explain the fundamental difference between physical “truth” and economic “models” to you.

    And let us try the following experiment. Please everybody here, take a look at Roslings 200 years (Gapminder):

    http://www.youtube.com/watch?v=jbkSRLYSojo

    Then just try to súmmarize in a very few sentences, what you have seen. Do not make a PhD thesis out of it, but if you derive some number(s) out it, nice. And what else you have seen.

    Please just post it here, without looking at the comments f others, but we obviously cant control that.

  71. Gravatar of genauer genauer
    13. February 2013 at 08:06

    I am especially interested in the comments of Scott, Elizier, David, Sarturos, and wait for them.

  72. Gravatar of genauer genauer
    13. February 2013 at 08:31

    And for those of you, who like this kind of puzzles,
    I have even an advanced, but black and white version:

    Chart 4 in:
    Technical Change and the Aggregate Production Function
    Author(s): Robert M. SolowReviewed work(s):Source: The Review of Economics and Statistics, Vol. 39, No. 3 (Aug., 1957), pp. 312-320Published by: The MIT PressStable URL: http://www.jstor.org/stable/1926047 .

    What is wrong with this?

  73. Gravatar of ssumner ssumner
    13. February 2013 at 08:32

    Saturos, You asked:

    “Put it another way – is the social value added of economics greater than its opportunity costs? Or would many of our great economists be better reemployed as mediocre physicists, from a social planner’s point of view?”

    Given the government subsidies to both mediocre economists and physicists perhaps both would be more productive doing something else. Great economists are far more productive in econ than they would be in physics.

  74. Gravatar of David Kagan David Kagan
    13. February 2013 at 11:46

    Hi Genauer,

    I’ve seen that video before. Rosling is wonderful at presenting and explaining data!

    I’m not exactly sure what you’re asking for here, but the chart and it’s evolution show two things quite clearly. There’s a strong correlation between income and lifespan, and there’s been an impressive overall shifting up and tilting flat of the relationship since the beginning of last century.

    How this relates to the interpretation of quantum theory is beyond me.

  75. Gravatar of David Kagan David Kagan
    13. February 2013 at 12:11

    Phil, I agree that the counterterms balance out divergences in loop diagrams. So yes, we are speaking about the same thing (more-or-less) but in slightly different ways. Though I think I was emphasizing the basic idea that renormalization isn’t likely to work when your coupling constant has a non-trivial dimension associated with it.

    Now I’m not sure I entirely understand what you’re saying regarding general covariance and the number of loops in your diagrams. I had thought that using background-field techniques, one could ensure that general covariance is preserved at any loop order. However, you will typically find that the counter-terms you have to add into the the theory are new combinations of the curvature tensor. This result also emerges from string-theoretic calculations.

    In other words, if you start with plain-vanilla Einstein gravity, where the Lagrangian density is proportional to the ricci curvature scalar R, you find that at one loop you have to add an R^2 term in order to be able to renormalize. This term is generally covariant, so that’s okay, but it means that quantization leads to a higher order curvature effect than you had in Einstein’s original theory. When you go to two loops, you can get terms of order R^3, and so on.

    So the issue, as I understand it, is simply that at every order you go (and equivalently, as you go up the energy ladder), you have to add more empirically determined constants to the theory in order to renormalize it. If you reason about this all the way to infinite energies, you get something that is unusable since you’d have to determine an infinite number of constants before making predictions. Thankfully, we don’t need to go up to infinite energies—a natural cut-off exists at the Planck scale, where we anticipate the nature of the whole theory changes to something like string theory (or some other approach to quantum gravity).

    I think that your intuition about dimensionful constants if a pretty good one. The idea being that the dimension of the coupling is a hint of some kind of underlying structure.

    We know how to do QFT on weakly curved spaces. The background field method is how it’s done. But in a deeper sense, we don’t know how to do QFT when spacetime itself can fluctuate violently. The only examples we have of theories that seem to probe the nature of quantum gravity relatively fully are the ones that are dual to non-gravitational qft’s via the AdS/CFT correspondence. The trick there though is that we don’t know how to track things like the worldlines of particles from the CFT (non-gravity) side, so we cannot start to answer questions like “what happens when an observer falls into a black hole”.

  76. Gravatar of genauer genauer
    13. February 2013 at 12:59

    @ David,

    the question was not supposed to have any thing to do with QM

  77. Gravatar of David Kagan David Kagan
    13. February 2013 at 15:12

    @ Genauer

    (i know!)

  78. Gravatar of David Kagan David Kagan
    17. February 2013 at 21:04

    Eliezer, thanks for showing me mercy. I have a decent memory, but it’s been a bit too long for that to help me much! Also, thanks for waiting patiently for this response. I’ve been a bit busy with teaching and some other things, and as you can see, I wanted to respond as thoroughly as possible.

    1) I’m glad (and unsurprised) that you don’t find the decision-theoretic approach to understanding probability in MWI appealing. Personally, I think that what they do is likely technically okay (I haven’t looked at it enough, but I’ll just take it as given that they do), I just think that layering the axioms of decision theory on top of the postulates of the many worlds interpretation is not really shedding much light on things. You may as well just assume the Born rule outright!

    2) I can’t speak to the mangled worlds approach. I do remember looking it up and reading a bit about it when I was going through your tutorial, but the details are not clear in my mind. I do seem to recall that it’s not complete yet though—or wasn’t at the time at any rate.

    I get the impression that you find collapse to always be an unnatural construct in the context of quantum theory. I claim that this needn’t be so. So let’s talk about collapse interpretations. You say, “Collapse interpretations make no use of unitarity”, but it depends on what you mean by a collapse interpretation (I’m also not 100% I understand the comment…the naive form of the Copenhagen interpretation makes use of unitarity, it’s just that collapse appears to be a non-unitary additional process. I assume that what you mean is that ultimately, collapse or something like it should flow out of unitary evolution. That’s not a crazy position at all, so I’ll go on assuming that that’s what you mean). If we’re talking about an interpretation that alters the mathematical form of quantum theory so that the wavefunction randomly collapses here and there, from time to time, then yeah, we’re talking about a totally different theory really. This approach has some adherents and a working model that some folks have been testing (this is the so-called GRW collapse theory). My money’s on quantum mechanics though. I’m guessing yours would be as well.

    There’s also what I like to call naive Copenhagen, wherein we think of their being some sharp quantum/classical divide and that the interaction across that divide causes collapse. This is not so much of a deviation from the mathematical structure of quantum mechanics as an additional set of postulates that basically say that quantum mechanics is incomplete without a classical world to explain measurements and their outcomes. While this approach is sort-of defensible, it requires you to believe that despite the fact that classical things are made out of quantum things, there’s some extra thing that happens somewhere that renders us classical. Okay, so that’s a hypothesis. Then there’s a prediction that arises: we’ll hit this divide at some point in our experiments, Anton Zellinger will win a Nobel, and we can all be happy. My money’s on quantum mechanics applying all the way up. Unitarity in this situation only applies to systems allowed to evolve without interacting with the classical-level objects.

    You can imagine other interpretations that are actually tweaks of the formal structure of quantum mechanics. Either because they alter the math, or because additional postulates alter the domain of applicability. Personally, I think that these things should be called “approaches” or alternate theories, since they don’t let quantum mechanics just be quantum mechanics.

    I think we want to restrict ourselves to discussing interpretations that maintain the structure of quantum mechanics and work from the standpoint that it is applicable on all scales.

    Among this way of interpreting things, there are some choices. One is collapse versus no-collapse. Another one that is prior to that is whether you believe that the wavefunction is part of the world or whether it is in the head of an observer. Is the wavefunction part of our ontology or is it epistemic? The terms I’ve seen thrown around are psi-ontic versus psi-epistemic. This naming scheme was naturally devised by psi-epistemic people so that they could tease the other view by calling them psi-ontologists (I’m not even joking here!).

    [Incidentally in your point number 4, you argue that Bell's theorem rules out the wavefunction as an epistemic quantity that describes our state of knowledge about a world satisfying local-realism. In fact, it rules out any *hidden variable* model that posits locality and that properties pre-exist their measurements. I'll respond in more depth when I get to point (4), but for now, let me just say that I don't see why dropping counterfactual-definiteness (which is the trick MWI uses) is obviously better than dropping (or weakening) locality (which is what any self-respecting hidden-variables theory must do). As I said, I'll talk about this more later.]

    Anyway, whether they be psi-epistemic or psi-ontic, there are collapse interpretations that are completely free of these sorts of distortions of quantum theory—let’s agree that these really are “interpretations” rather than actually alternate theories.

    As an existence proof, I bring up Bohmian mechanics (a psi-ontic model if ever there was one, though with subtleties!). It can be formulated to agree exactly with the quantum formalism. And yet, there is a form of collapse since in Bohmian mechanics, uncertainty arises from ignorance of the initial state of everything. Once we determine the position of the particle, there is no more uncertainty about it (until it’s perturbed by something that we’re not tracking), so your epistemic probability scheme “collapses” to a delta function and your ontological wavefunction is altered by the physical act of measurement (probably via something like decoherence—I actually don’t know the details here since I’m not an expert by any stretch of the imagination).

    Now, I’ve got qualms with Bohmian mechanics. I think it masks more than it reveals about the nature of quantum theory (in some ways, it’s designed to do so). So I am not a Bohmian. However—and I’m jumping around a bit here—I’d be careful about using Occam’s Razor to do violence to Bohm (poor Bohm!). I worry that what individuals find to be conceptually clear and hence, simple, is largely a matter of familiarity and taste in these types of discussions. As you know, people throw around Occam’s Razor in trying to slice up MWI (who needs all these universes! I say cut them with Occam’s Razor!). I don’t think that those arguments are compelling, but hey, I don’t necessarily think that they are compelling with regards to Bohm either (although, yes, I am more sympathetic to MWI than Bohm afterall).

    (Incidentally, I think Bohm’s theory can play a useful role in getting you to think through certain types of problems that you might encounter. Plus, it can act as a kind-of safety blanket, since as a young child you go into physics due to it’s precision and the fact that in principle everything is predictable. Then quantum mechanics comes along and causes you to go into a young-adult-life-crisis where you start questioning everything you thought you knew about yourself, the universe, God, no-God, whatever. Bohm comes in and says “No! Don’t panic! Particles exist, they have trajectories, it’s all okay. We are just limited in our ability to predict these things due to a conserved amount of initial ignorance about the state of the universe!” This makes you happy. Then you get older and you realize that uncertainty is the way of things and you just have to deal with it, so into the bin goes the safety blanket).

    (Okay, I got a little carried away there!)

    So I don’t think you can use unitarity to rule out all collapse-type interpretations. There are ways of making these things compatible. I also worry whenever Occam’s Razor is invoked, because often its use is more revelatory about the tastes of the user than the merits of the things its being invoked against.

    3) You said “more generally, no amount of single-world interpreting gets us any closer to understanding the Born probabilities.”

    What exactly do you mean by “understanding the Born probabilities”? Are you referring to setting up an interpretation that does not postulate them and then deriving them? Are you talking about the related but different problem of understanding these things as probabilities (a very difficult problem since you are then trying to answer the question of what probabilities are)?

    You go on to ask (I’ll paraphrase) why it should be so much better to have a single world left behind after measurement, rather than a population of worlds with different results. How does it help explain the origin of Born statistics in particular?

    I think that the answer to your question is basically that it is a lot more straightforward to understand what any sorts of probabilities mean in a situation where counterfactual definiteness holds. Furthermore, it’s a lot clearer how one should think about experimental results and how to falsify theories when we view the world as one with definite outcomes. I think that that’s the key argument, and it’s in addressing those issues that MWI itself racks up a lot of complexity.

    To put it another way, I could make precisely the same statements about the ordinary application of probability theory. Why shouldn’t a classical die roll be thought of as splitting the universe into 6 different pieces (or whatever) in which any of the possibilities could happen? You might claim that the dynamics is deterministic, but chaotic effects can make it impossible to really churn out deterministic answers (they effectively put classical physics on a similar footing to Bohmian mechanics—you have no way to ever determine the initial conditions accurately enough). So why not say that classical probabilities also lead to many worlds? The most straightforward reason not to (and it’s a choice, not a rule) is that it makes it a lot harder to understand what these probabilities mean. Again, having definite outcomes makes this problem easier to deal with.

    Furthermore, I think having a single definite outcome better positions you to attack the problem of Born probabilities.

    One way to do this is to actually start from the Born probabilities and attempt to see how much of the structure of quantum mechanics can be derived from that (perhaps plus a bit of additional structure). One programme in this vein—certainly not complete—is Chris Fuchs’ (he’s a professor at Perimeter), in which he recasts the Born rule in a form that is very similar to the law of total probability in ordinary probability theory. From this form he’s able to derive a number of conclusions about the structure of quantum mechanics (though he cannot derive the full theory from this one starting point just yet).

    Another approach may involve taking density matrices as your primary descriptors of a system’s probabilities. What’s nice about this is that the Born statistics emerge from certain unique properties of density matrices. Such an approach can also makes the clearest contact with decoherence, when formulated appropriately.

    Turning your questions around, I don’t quite see why it’s necessarily the case that one treats amplitudes as physical in the way that you are suggesting. Not many people have a problem with a classical probability distribution collapsing to some particular outcome after a measurement occurs—we just call that updating. Why can’t we think of quantum probability in a similar manner?

    In the context of MWI, we have a serious issue, because MWI sets itself the task of using the wavefunction as an actual, physical entity that represents the state of the whole universe. From this perspective, you really need to carefully describe what the Born probabilities are, even if you include them as an additional postulate. You have to get into explanations of self-locating probabilities and whatnot. I’m not saying that that’s impossible, I’m just saying, it spoils some of the original sleekness of many worlds, which is its major source of appeal.

    You also get entangled in the great debate about the meaning of probability itself, which I think should ideally be kept distinct from questions about the meaning of quantum mechanics (what’s more nettlesome than one deep mystery? Taking two of them and scrambling them up!).

    I suppose what I’m trying to say is that approaches like MWI have to grapple with the nature of what probabilities are, which is a very hard problem. On top of that they either have to derive or add as an additional postulate the Born probability, which only adds to the oddness of trying to understand probabilities in these contexts. Other approaches, that basically try to separate out the problem of probability from the rest of quantum theory are at least cleaner from that perspective. I hate to return to Bohmian mechanics since I’m not a fan, but at least the meaning of probability is simple and clear in that approach, it’s a way of formalizing our ignorance.

    4) That the wavefunction is an epistemic description of our uncertainty about some deeper, locally causal, single world is decisively ruled out by Bell’s Theorem. I can’t quite say that everyone knows this part, but everyone knows the math and I think a majority of physicists would agree with what I just said, though they might phrase it differently since they wouldn’t be acquainted with Judea Pearl’s standard definition of local causality which is more something that probability theorists know.

    4) If we insist on an epistemc or ontic conception of the wavefunction that is local and real and maintains counterfactual-definiteness, then those interpretations are ruled out. MWI gets around this by dropping counterfactual definiteness.

    But you could also weaken your notion of locality. For example, you could simply demand that information has to be transmitted in a manner that respects locality or causality, but non-local things can occur if no information gain is possible. For example, in a Bell-type experiment, Alice and Bob can only determine that their systems were entangled after-the-fact. They need to gather data and compare in order to rule out the possibility of a classical correlation in favor of a quantum entanglement. None of their measurements during the experiment can be used to transmit information superluminally (i.e. acausally).

    It’s not obvious that dropping locality is a much worse option than dropping counterfactual definiteness. Bell can’t save you from considering alternate interpretations! Even the ones that take the wavefunction as an epistemic object rather than as an ontological one.

    There are indeed serious problems one has to confront if you want to use the wavefunction as an epistemic object. For example: if you have a composite system, typically you can write down the wavefunction for the entire thing, but it’s not necessarily the case that the wavefunction cleanly factorizes so as to give you a sensible definition of wavefunction for the pieces. In that case, it’s unclear (to me anyway) how I am supposed to use wavefunctions as epistemic objects to encode my knowledge-state about the subsystems.

    The easiest way around this that I know of is to forget about wavefunctions and work at the level of density matrices. These behave sort-of like a probability operator (akin to the energy being represented as a Hamiltonian operator), but it can’t work precisely like all the other operators (there are technical differences that I won’t delve into here). Anyway, there is a unique prescription for assigning a density operator to any system you wish to investigate. Furthermore, if you want to go down a more epistemic route, the density operator is a natural object since it is traditionally a way of encoding “classical” uncertainty that sits on top of the quantum kind. However, this distinction between classical and quantum uncertainty does not have to be maintained, and one can instead see density matrices as unifying both. I don’t want to get bogged down in details, but I just want to put this out there as another way to take an epistemic approach to quantum probabilities.

    As an aside, I’m actually pretty interested in Judea Pearl’s work on causality—I have your treatment of it on Lesswrong bookmarked for a time when I am not so busy. In fact, it’d be great to read his book…but again too busy!

    But the reason I wanted to talk about Pearl is actually because his influence is starting to be felt at least a little bit in a corner of the foundations of quantum mechanics community. I recommend checking out Robert Spekkens’ essay on kinematics versus dynamics (you can find it via Google. The title escapes me. I believe it won an fQXI award). His point is that the dividing line between kinematics and dynamics is a choice and that the more invariant notion to use is that of causal structure (a la Pearl). He is actively interested in figuring out how to properly quantize these ideas. I figured you’d find that interesting!

    5) Again, I think that the complexity-penalty calculus is not quite so straightforward. MWI does indeed seemingly begin with fewer postulates, but then you have to construct elaborate arguments for why it’s okay to use Born statistics to interpret your experiments. Again, even if you add Born as an additional postulate, explaining what you mean by probabilities here adds complexity to the approach.

    And MWI is not the only approach to quantum theory that comes from applying the same rules at all levels. Developing quantum theory as primarily a generalized form of probability theory also allows you to work with it at all levels, and it provides a natural reason for why you can throw out unobserved branches (because it is exactly analogous to what you do in classical probability theory).

    6) “Hypothesis non yet fingo” is such an obscene sounding expression!

    But turning to the matter of the preferred basis—Now if I’m reading you correctly, you’re saying tht the preferred basis problem is an artifact of taking the worlds as basic ingredients rather than as something that emerges from the description in a natural way. I agree to a certain extent. In some ways the worst thing to happen to Everett’s “relative state” interpretation was having it renamed “many worlds” since that places the emphasis on a rather sensational, but ultimately secondary aspect of the interpretation.

    (I’d be careful about analogizing this with notions of symmetry in relativity or newtonian mechanics. While there is a way of attacking the preferred basis issue using symmetry [Zurek's notion of envariance, if I recall correctly] it is of a rather different sort of flavor.)

    I think there are several approaches to dealing with the preferred basis issue, one of which is sort-of suggested by your comment (again, if I’m reading you correctly). That is, there is nothing fundamental about this particular decomposition of Psi (the universal wavefunction). Instead, it is merely the decomposition compatible with our perception of how the Hilbert space breaks up into subsystems. It seems to me that this has to do with dynamics—what ends up being weakly coupled to what so that separation into subsystems is a useful thing to do. So while I don’t think that the question can be wished away, I do think that there are ways of trying to get out of it with out larding on more interpretational complexity.

    I don’t want to suggest that MWI isn’t a valid approach. I think that it is, and I also think that it has gained a great deal of popularity in the physics community because it is conceptually clarifying in some important respects. But it is false to suggest that it is the only principled way to do quantum mechanics, or even the most minimalistic principled way to do it. As I’ve alluded to several times in this response, there are several other approaches, all with their merits, that don’t differ too strongly (to my mind) in their level of complexity from the many worlds approach. Some of them have the added benefit of cleanly separating the problems of interpreting probabilities themselves from the problem of formulating quantum mechanics. This is one area where many worlds runs into severe difficulties, and is probably my primary reason for feeling that it does not deserve the status of a consensus position.

    Whew! I’m sure I’ve left a lot unsaid that probably should be said…but this is getting rather too lengthy, so I will stop here.

  79. Gravatar of Neal Neal
    18. February 2013 at 04:38

    If you all will permit a late post, here’s another physics analogy in economics: accounting identities are like physical conservation laws. Y will ALWAYS equal C + G + I + NX; MV will ALWAYS equal Py; total assets + total liabilities will ALWAYS equal zero; and so forth.

  80. Gravatar of David Kagan David Kagan
    18. February 2013 at 17:30

    Hi Neal,

    I think I’d disagree (though I’m quite naive regarding econ). As I understand it

    Y = C + G + I + NX

    ought to really be thought of as a definition. It’s true because it’s true.

    Energy conservation on the other hand is not a definition. It is a law that arises from symmetries in nature (in this case, systems that are symmetrical through time).

    So I’d say that the accounting identity above is more like

    p = mv

    as a definition of momentum.

    But I’d love to be corrected if I’m in error.

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